Integrand size = 718, antiderivative size = 24 \[ \int \frac {-64-768 x^2+256 x^3+x^5+20 x^7-5 x^8+160 x^9-80 x^{10}+650 x^{11}-480 x^{12}+1400 x^{13}-1290 x^{14}+1504 x^{15}-1360 x^{16}+645 x^{17}-160 x^{18}+20 x^{19}-x^{20}+e^8 \left (160 x^9-80 x^{10}+1930 x^{11}-1440 x^{12}+8040 x^{13}-7710 x^{14}+13120 x^{15}-13280 x^{16}+6430 x^{17}-1600 x^{18}+200 x^{19}-10 x^{20}\right )+e^{16} \left (1280 x^{13}-1280 x^{14}+5600 x^{15}-6480 x^{16}+3205 x^{17}-800 x^{18}+100 x^{19}-5 x^{20}\right )+e^{20} \left (-1024 x^{15}+1280 x^{16}-640 x^{17}+160 x^{18}-20 x^{19}+x^{20}\right )+e^4 \left (768 x^2-256 x^3-20 x^7+5 x^8-320 x^9+160 x^{10}-1940 x^{11}+1440 x^{12}-5480 x^{13}+5150 x^{14}-7040 x^{15}+6720 x^{16}-3220 x^{17}+800 x^{18}-100 x^{19}+5 x^{20}\right )+e^{12} \left (-640 x^{11}+480 x^{12}-5240 x^{13}+5130 x^{14}-12160 x^{15}+13120 x^{16}-6420 x^{17}+1600 x^{18}-200 x^{19}+10 x^{20}\right )}{x^5+20 x^7-5 x^8+160 x^9-80 x^{10}+650 x^{11}-480 x^{12}+1400 x^{13}-1290 x^{14}+1504 x^{15}-1360 x^{16}+645 x^{17}-160 x^{18}+20 x^{19}-x^{20}+e^8 \left (160 x^9-80 x^{10}+1930 x^{11}-1440 x^{12}+8040 x^{13}-7710 x^{14}+13120 x^{15}-13280 x^{16}+6430 x^{17}-1600 x^{18}+200 x^{19}-10 x^{20}\right )+e^{16} \left (1280 x^{13}-1280 x^{14}+5600 x^{15}-6480 x^{16}+3205 x^{17}-800 x^{18}+100 x^{19}-5 x^{20}\right )+e^{20} \left (-1024 x^{15}+1280 x^{16}-640 x^{17}+160 x^{18}-20 x^{19}+x^{20}\right )+e^4 \left (-20 x^7+5 x^8-320 x^9+160 x^{10}-1940 x^{11}+1440 x^{12}-5480 x^{13}+5150 x^{14}-7040 x^{15}+6720 x^{16}-3220 x^{17}+800 x^{18}-100 x^{19}+5 x^{20}\right )+e^{12} \left (-640 x^{11}+480 x^{12}-5240 x^{13}+5130 x^{14}-12160 x^{15}+13120 x^{16}-6420 x^{17}+1600 x^{18}-200 x^{19}+10 x^{20}\right )} \, dx=x+\frac {16}{\left (x+(-4+x) x^2 \left (-x+e^4 x\right )\right )^4} \]
\[ \int \frac {-64-768 x^2+256 x^3+x^5+20 x^7-5 x^8+160 x^9-80 x^{10}+650 x^{11}-480 x^{12}+1400 x^{13}-1290 x^{14}+1504 x^{15}-1360 x^{16}+645 x^{17}-160 x^{18}+20 x^{19}-x^{20}+e^8 \left (160 x^9-80 x^{10}+1930 x^{11}-1440 x^{12}+8040 x^{13}-7710 x^{14}+13120 x^{15}-13280 x^{16}+6430 x^{17}-1600 x^{18}+200 x^{19}-10 x^{20}\right )+e^{16} \left (1280 x^{13}-1280 x^{14}+5600 x^{15}-6480 x^{16}+3205 x^{17}-800 x^{18}+100 x^{19}-5 x^{20}\right )+e^{20} \left (-1024 x^{15}+1280 x^{16}-640 x^{17}+160 x^{18}-20 x^{19}+x^{20}\right )+e^4 \left (768 x^2-256 x^3-20 x^7+5 x^8-320 x^9+160 x^{10}-1940 x^{11}+1440 x^{12}-5480 x^{13}+5150 x^{14}-7040 x^{15}+6720 x^{16}-3220 x^{17}+800 x^{18}-100 x^{19}+5 x^{20}\right )+e^{12} \left (-640 x^{11}+480 x^{12}-5240 x^{13}+5130 x^{14}-12160 x^{15}+13120 x^{16}-6420 x^{17}+1600 x^{18}-200 x^{19}+10 x^{20}\right )}{x^5+20 x^7-5 x^8+160 x^9-80 x^{10}+650 x^{11}-480 x^{12}+1400 x^{13}-1290 x^{14}+1504 x^{15}-1360 x^{16}+645 x^{17}-160 x^{18}+20 x^{19}-x^{20}+e^8 \left (160 x^9-80 x^{10}+1930 x^{11}-1440 x^{12}+8040 x^{13}-7710 x^{14}+13120 x^{15}-13280 x^{16}+6430 x^{17}-1600 x^{18}+200 x^{19}-10 x^{20}\right )+e^{16} \left (1280 x^{13}-1280 x^{14}+5600 x^{15}-6480 x^{16}+3205 x^{17}-800 x^{18}+100 x^{19}-5 x^{20}\right )+e^{20} \left (-1024 x^{15}+1280 x^{16}-640 x^{17}+160 x^{18}-20 x^{19}+x^{20}\right )+e^4 \left (-20 x^7+5 x^8-320 x^9+160 x^{10}-1940 x^{11}+1440 x^{12}-5480 x^{13}+5150 x^{14}-7040 x^{15}+6720 x^{16}-3220 x^{17}+800 x^{18}-100 x^{19}+5 x^{20}\right )+e^{12} \left (-640 x^{11}+480 x^{12}-5240 x^{13}+5130 x^{14}-12160 x^{15}+13120 x^{16}-6420 x^{17}+1600 x^{18}-200 x^{19}+10 x^{20}\right )} \, dx=\int \frac {-64-768 x^2+256 x^3+x^5+20 x^7-5 x^8+160 x^9-80 x^{10}+650 x^{11}-480 x^{12}+1400 x^{13}-1290 x^{14}+1504 x^{15}-1360 x^{16}+645 x^{17}-160 x^{18}+20 x^{19}-x^{20}+e^8 \left (160 x^9-80 x^{10}+1930 x^{11}-1440 x^{12}+8040 x^{13}-7710 x^{14}+13120 x^{15}-13280 x^{16}+6430 x^{17}-1600 x^{18}+200 x^{19}-10 x^{20}\right )+e^{16} \left (1280 x^{13}-1280 x^{14}+5600 x^{15}-6480 x^{16}+3205 x^{17}-800 x^{18}+100 x^{19}-5 x^{20}\right )+e^{20} \left (-1024 x^{15}+1280 x^{16}-640 x^{17}+160 x^{18}-20 x^{19}+x^{20}\right )+e^4 \left (768 x^2-256 x^3-20 x^7+5 x^8-320 x^9+160 x^{10}-1940 x^{11}+1440 x^{12}-5480 x^{13}+5150 x^{14}-7040 x^{15}+6720 x^{16}-3220 x^{17}+800 x^{18}-100 x^{19}+5 x^{20}\right )+e^{12} \left (-640 x^{11}+480 x^{12}-5240 x^{13}+5130 x^{14}-12160 x^{15}+13120 x^{16}-6420 x^{17}+1600 x^{18}-200 x^{19}+10 x^{20}\right )}{x^5+20 x^7-5 x^8+160 x^9-80 x^{10}+650 x^{11}-480 x^{12}+1400 x^{13}-1290 x^{14}+1504 x^{15}-1360 x^{16}+645 x^{17}-160 x^{18}+20 x^{19}-x^{20}+e^8 \left (160 x^9-80 x^{10}+1930 x^{11}-1440 x^{12}+8040 x^{13}-7710 x^{14}+13120 x^{15}-13280 x^{16}+6430 x^{17}-1600 x^{18}+200 x^{19}-10 x^{20}\right )+e^{16} \left (1280 x^{13}-1280 x^{14}+5600 x^{15}-6480 x^{16}+3205 x^{17}-800 x^{18}+100 x^{19}-5 x^{20}\right )+e^{20} \left (-1024 x^{15}+1280 x^{16}-640 x^{17}+160 x^{18}-20 x^{19}+x^{20}\right )+e^4 \left (-20 x^7+5 x^8-320 x^9+160 x^{10}-1940 x^{11}+1440 x^{12}-5480 x^{13}+5150 x^{14}-7040 x^{15}+6720 x^{16}-3220 x^{17}+800 x^{18}-100 x^{19}+5 x^{20}\right )+e^{12} \left (-640 x^{11}+480 x^{12}-5240 x^{13}+5130 x^{14}-12160 x^{15}+13120 x^{16}-6420 x^{17}+1600 x^{18}-200 x^{19}+10 x^{20}\right )} \, dx \]
Integrate[(-64 - 768*x^2 + 256*x^3 + x^5 + 20*x^7 - 5*x^8 + 160*x^9 - 80*x ^10 + 650*x^11 - 480*x^12 + 1400*x^13 - 1290*x^14 + 1504*x^15 - 1360*x^16 + 645*x^17 - 160*x^18 + 20*x^19 - x^20 + E^8*(160*x^9 - 80*x^10 + 1930*x^1 1 - 1440*x^12 + 8040*x^13 - 7710*x^14 + 13120*x^15 - 13280*x^16 + 6430*x^1 7 - 1600*x^18 + 200*x^19 - 10*x^20) + E^16*(1280*x^13 - 1280*x^14 + 5600*x ^15 - 6480*x^16 + 3205*x^17 - 800*x^18 + 100*x^19 - 5*x^20) + E^20*(-1024* x^15 + 1280*x^16 - 640*x^17 + 160*x^18 - 20*x^19 + x^20) + E^4*(768*x^2 - 256*x^3 - 20*x^7 + 5*x^8 - 320*x^9 + 160*x^10 - 1940*x^11 + 1440*x^12 - 54 80*x^13 + 5150*x^14 - 7040*x^15 + 6720*x^16 - 3220*x^17 + 800*x^18 - 100*x ^19 + 5*x^20) + E^12*(-640*x^11 + 480*x^12 - 5240*x^13 + 5130*x^14 - 12160 *x^15 + 13120*x^16 - 6420*x^17 + 1600*x^18 - 200*x^19 + 10*x^20))/(x^5 + 2 0*x^7 - 5*x^8 + 160*x^9 - 80*x^10 + 650*x^11 - 480*x^12 + 1400*x^13 - 1290 *x^14 + 1504*x^15 - 1360*x^16 + 645*x^17 - 160*x^18 + 20*x^19 - x^20 + E^8 *(160*x^9 - 80*x^10 + 1930*x^11 - 1440*x^12 + 8040*x^13 - 7710*x^14 + 1312 0*x^15 - 13280*x^16 + 6430*x^17 - 1600*x^18 + 200*x^19 - 10*x^20) + E^16*( 1280*x^13 - 1280*x^14 + 5600*x^15 - 6480*x^16 + 3205*x^17 - 800*x^18 + 100 *x^19 - 5*x^20) + E^20*(-1024*x^15 + 1280*x^16 - 640*x^17 + 160*x^18 - 20* x^19 + x^20) + E^4*(-20*x^7 + 5*x^8 - 320*x^9 + 160*x^10 - 1940*x^11 + 144 0*x^12 - 5480*x^13 + 5150*x^14 - 7040*x^15 + 6720*x^16 - 3220*x^17 + 800*x ^18 - 100*x^19 + 5*x^20) + E^12*(-640*x^11 + 480*x^12 - 5240*x^13 + 5130*x ^14 - 12160*x^15 + 13120*x^16 - 6420*x^17 + 1600*x^18 - 200*x^19 + 10*x^20 )),x]
Integrate[(-64 - 768*x^2 + 256*x^3 + x^5 + 20*x^7 - 5*x^8 + 160*x^9 - 80*x ^10 + 650*x^11 - 480*x^12 + 1400*x^13 - 1290*x^14 + 1504*x^15 - 1360*x^16 + 645*x^17 - 160*x^18 + 20*x^19 - x^20 + E^8*(160*x^9 - 80*x^10 + 1930*x^1 1 - 1440*x^12 + 8040*x^13 - 7710*x^14 + 13120*x^15 - 13280*x^16 + 6430*x^1 7 - 1600*x^18 + 200*x^19 - 10*x^20) + E^16*(1280*x^13 - 1280*x^14 + 5600*x ^15 - 6480*x^16 + 3205*x^17 - 800*x^18 + 100*x^19 - 5*x^20) + E^20*(-1024* x^15 + 1280*x^16 - 640*x^17 + 160*x^18 - 20*x^19 + x^20) + E^4*(768*x^2 - 256*x^3 - 20*x^7 + 5*x^8 - 320*x^9 + 160*x^10 - 1940*x^11 + 1440*x^12 - 54 80*x^13 + 5150*x^14 - 7040*x^15 + 6720*x^16 - 3220*x^17 + 800*x^18 - 100*x ^19 + 5*x^20) + E^12*(-640*x^11 + 480*x^12 - 5240*x^13 + 5130*x^14 - 12160 *x^15 + 13120*x^16 - 6420*x^17 + 1600*x^18 - 200*x^19 + 10*x^20))/(x^5 + 2 0*x^7 - 5*x^8 + 160*x^9 - 80*x^10 + 650*x^11 - 480*x^12 + 1400*x^13 - 1290 *x^14 + 1504*x^15 - 1360*x^16 + 645*x^17 - 160*x^18 + 20*x^19 - x^20 + E^8 *(160*x^9 - 80*x^10 + 1930*x^11 - 1440*x^12 + 8040*x^13 - 7710*x^14 + 1312 0*x^15 - 13280*x^16 + 6430*x^17 - 1600*x^18 + 200*x^19 - 10*x^20) + E^16*( 1280*x^13 - 1280*x^14 + 5600*x^15 - 6480*x^16 + 3205*x^17 - 800*x^18 + 100 *x^19 - 5*x^20) + E^20*(-1024*x^15 + 1280*x^16 - 640*x^17 + 160*x^18 - 20* x^19 + x^20) + E^4*(-20*x^7 + 5*x^8 - 320*x^9 + 160*x^10 - 1940*x^11 + 144 0*x^12 - 5480*x^13 + 5150*x^14 - 7040*x^15 + 6720*x^16 - 3220*x^17 + 800*x ^18 - 100*x^19 + 5*x^20) + E^12*(-640*x^11 + 480*x^12 - 5240*x^13 + 513...
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int \frac {-x^{20}+20 x^{19}-160 x^{18}+645 x^{17}-1360 x^{16}+1504 x^{15}-1290 x^{14}+1400 x^{13}-480 x^{12}+650 x^{11}-80 x^{10}+160 x^9-5 x^8+20 x^7+x^5+256 x^3-768 x^2+e^{20} \left (x^{20}-20 x^{19}+160 x^{18}-640 x^{17}+1280 x^{16}-1024 x^{15}\right )+e^{16} \left (-5 x^{20}+100 x^{19}-800 x^{18}+3205 x^{17}-6480 x^{16}+5600 x^{15}-1280 x^{14}+1280 x^{13}\right )+e^{12} \left (10 x^{20}-200 x^{19}+1600 x^{18}-6420 x^{17}+13120 x^{16}-12160 x^{15}+5130 x^{14}-5240 x^{13}+480 x^{12}-640 x^{11}\right )+e^8 \left (-10 x^{20}+200 x^{19}-1600 x^{18}+6430 x^{17}-13280 x^{16}+13120 x^{15}-7710 x^{14}+8040 x^{13}-1440 x^{12}+1930 x^{11}-80 x^{10}+160 x^9\right )+e^4 \left (5 x^{20}-100 x^{19}+800 x^{18}-3220 x^{17}+6720 x^{16}-7040 x^{15}+5150 x^{14}-5480 x^{13}+1440 x^{12}-1940 x^{11}+160 x^{10}-320 x^9+5 x^8-20 x^7-256 x^3+768 x^2\right )-64}{-x^{20}+20 x^{19}-160 x^{18}+645 x^{17}-1360 x^{16}+1504 x^{15}-1290 x^{14}+1400 x^{13}-480 x^{12}+650 x^{11}-80 x^{10}+160 x^9-5 x^8+20 x^7+x^5+e^{20} \left (x^{20}-20 x^{19}+160 x^{18}-640 x^{17}+1280 x^{16}-1024 x^{15}\right )+e^{16} \left (-5 x^{20}+100 x^{19}-800 x^{18}+3205 x^{17}-6480 x^{16}+5600 x^{15}-1280 x^{14}+1280 x^{13}\right )+e^{12} \left (10 x^{20}-200 x^{19}+1600 x^{18}-6420 x^{17}+13120 x^{16}-12160 x^{15}+5130 x^{14}-5240 x^{13}+480 x^{12}-640 x^{11}\right )+e^8 \left (-10 x^{20}+200 x^{19}-1600 x^{18}+6430 x^{17}-13280 x^{16}+13120 x^{15}-7710 x^{14}+8040 x^{13}-1440 x^{12}+1930 x^{11}-80 x^{10}+160 x^9\right )+e^4 \left (5 x^{20}-100 x^{19}+800 x^{18}-3220 x^{17}+6720 x^{16}-7040 x^{15}+5150 x^{14}-5480 x^{13}+1440 x^{12}-1940 x^{11}+160 x^{10}-320 x^9+5 x^8-20 x^7\right )} \, dx\) |
| \(\Big \downarrow \) 2026 |
| \(\displaystyle \int \frac {-x^{20}+20 x^{19}-160 x^{18}+645 x^{17}-1360 x^{16}+1504 x^{15}-1290 x^{14}+1400 x^{13}-480 x^{12}+650 x^{11}-80 x^{10}+160 x^9-5 x^8+20 x^7+x^5+256 x^3-768 x^2+e^{20} \left (x^{20}-20 x^{19}+160 x^{18}-640 x^{17}+1280 x^{16}-1024 x^{15}\right )+e^{16} \left (-5 x^{20}+100 x^{19}-800 x^{18}+3205 x^{17}-6480 x^{16}+5600 x^{15}-1280 x^{14}+1280 x^{13}\right )+e^{12} \left (10 x^{20}-200 x^{19}+1600 x^{18}-6420 x^{17}+13120 x^{16}-12160 x^{15}+5130 x^{14}-5240 x^{13}+480 x^{12}-640 x^{11}\right )+e^8 \left (-10 x^{20}+200 x^{19}-1600 x^{18}+6430 x^{17}-13280 x^{16}+13120 x^{15}-7710 x^{14}+8040 x^{13}-1440 x^{12}+1930 x^{11}-80 x^{10}+160 x^9\right )+e^4 \left (5 x^{20}-100 x^{19}+800 x^{18}-3220 x^{17}+6720 x^{16}-7040 x^{15}+5150 x^{14}-5480 x^{13}+1440 x^{12}-1940 x^{11}+160 x^{10}-320 x^9+5 x^8-20 x^7-256 x^3+768 x^2\right )-64}{x^5 \left (-\left (1-e^4\right )^5 x^{15}+20 \left (1-e^4\right )^5 x^{14}-160 \left (1-e^4\right )^5 x^{13}+5 \left (129-128 e^4\right ) \left (1-e^4\right )^4 x^{12}-80 \left (17-16 e^4\right ) \left (1-e^4\right )^4 x^{11}+32 \left (47-32 e^4\right ) \left (1-e^4\right )^4 x^{10}-10 \left (129-128 e^4\right ) \left (1-e^4\right )^3 x^9+40 \left (35-32 e^4\right ) \left (1-e^4\right )^3 x^8-480 \left (1-e^4\right )^3 x^7+10 \left (65-64 e^4\right ) \left (1-e^4\right )^2 x^6-80 \left (1-e^4\right )^2 x^5+160 \left (1-e^4\right )^2 x^4-5 \left (1-e^4\right ) x^3+20 \left (1-e^4\right ) x^2+1\right )}dx\) |
| \(\Big \downarrow \) 2462 |
| \(\displaystyle \int \left (\frac {5 e^4 \left (1+\frac {-1-10 e^8+10 e^{12}-5 e^{16}+e^{20}}{5 e^4}\right ) x^{15}}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {20 \left (1-e^4 \left (5-10 e^4+10 e^8-5 e^{12}+e^{16}\right )\right ) x^{14}}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {800 e^4 \left (1+\frac {-1-10 e^8+10 e^{12}-5 e^{16}+e^{20}}{5 e^4}\right ) x^{13}}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {645 \left (1-\frac {1}{129} e^4 \left (644-1286 e^4+1284 e^8-641 e^{12}+128 e^{16}\right )\right ) x^{12}}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {6720 e^4 \left (1-\frac {17+166 e^8-164 e^{12}+81 e^{16}-16 e^{20}}{84 e^4}\right ) x^{11}}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {1504 \left (1-\frac {1}{47} e^4 \left (220-410 e^4+380 e^8-175 e^{12}+32 e^{16}\right )\right ) x^{10}}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {5150 e^4 \left (1-\frac {129+771 e^8-513 e^{12}+128 e^{16}}{515 e^4}\right ) x^9}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {1400 \left (1+\frac {1}{35} e^4 \left (-137+201 e^4-131 e^8+32 e^{12}\right )\right ) x^8}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {1440 e^4 \left (1+\frac {-1-3 e^8+e^{12}}{3 e^4}\right ) x^7}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {650 \left (1-\frac {1}{65} e^4 \left (194-193 e^4+64 e^8\right )\right ) x^6}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {160 e^4 \left (1-\frac {1+e^8}{2 e^4}\right ) x^5}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {160 \left (1+e^4 \left (-2+e^4\right )\right ) x^4}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {5 \left (1-\frac {1}{e^4}\right ) e^4 x^3}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {20 \left (1-e^4\right ) x^2}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {1}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {256 \left (1-e^4\right )}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5 x^2}+\frac {768 \left (1-\frac {1}{e^4}\right ) e^4}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5 x^3}+\frac {64}{\left (\left (1-e^4\right ) x^3-4 \left (1-e^4\right ) x^2-1\right )^5 x^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (e^4-1\right )^5 x^{20}-20 \left (e^4-1\right )^5 x^{19}+160 \left (e^4-1\right )^5 x^{18}-5 \left (e^4-1\right )^4 \left (128 e^4-129\right ) x^{17}+80 \left (e^4-1\right )^4 \left (16 e^4-17\right ) x^{16}-32 \left (e^4-1\right )^4 \left (32 e^4-47\right ) x^{15}-10 \left (e^4-1\right )^3 \left (128 e^4-129\right ) x^{14}+40 \left (e^4-1\right )^3 \left (32 e^4-35\right ) x^{13}+480 \left (e^4-1\right )^3 x^{12}-10 \left (e^4-1\right )^2 \left (64 e^4-65\right ) x^{11}-80 \left (e^4-1\right )^2 x^{10}+160 \left (e^4-1\right )^2 x^9+5 \left (e^4-1\right ) x^8-20 \left (e^4-1\right ) x^7+x^5-256 \left (e^4-1\right ) x^3+768 \left (e^4-1\right ) x^2-64}{x^5 \left (\left (e^4-1\right ) x^3-4 \left (e^4-1\right ) x^2+1\right )^5}dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {\left (e^4-1\right )^5 x^{20}-20 \left (e^4-1\right )^5 x^{19}+160 \left (e^4-1\right )^5 x^{18}-5 \left (e^4-1\right )^4 \left (128 e^4-129\right ) x^{17}+80 \left (e^4-1\right )^4 \left (16 e^4-17\right ) x^{16}-32 \left (e^4-1\right )^4 \left (32 e^4-47\right ) x^{15}-10 \left (e^4-1\right )^3 \left (128 e^4-129\right ) x^{14}+40 \left (e^4-1\right )^3 \left (32 e^4-35\right ) x^{13}+480 \left (e^4-1\right )^3 x^{12}-10 \left (e^4-1\right )^2 \left (64 e^4-65\right ) x^{11}-80 \left (e^4-1\right )^2 x^{10}+160 \left (e^4-1\right )^2 x^9+5 \left (e^4-1\right ) x^8-20 \left (e^4-1\right ) x^7+x^5-256 \left (e^4-1\right ) x^3+768 \left (e^4-1\right ) x^2-64}{x^5 \left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {5 \left (e^4-1\right ) x^3}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {20 \left (1-e^4\right ) x^2}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {1}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {256 \left (1-e^4\right )}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5 x^2}+\frac {768 \left (e^4-1\right )}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5 x^3}+\frac {\left (e^4-1\right )^5 x^{15}}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {20 \left (1-e^4\right )^5 x^{14}}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {160 \left (e^4-1\right )^5 x^{13}}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {5 \left (129-128 e^4\right ) \left (1-e^4\right )^4 x^{12}}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {80 \left (1-e^4\right )^4 \left (16 e^4-17\right ) x^{11}}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {32 \left (47-32 e^4\right ) \left (1-e^4\right )^4 x^{10}}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {10 \left (1-e^4\right )^3 \left (128 e^4-129\right ) x^9}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {40 \left (35-32 e^4\right ) \left (1-e^4\right )^3 x^8}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {480 \left (e^4-1\right )^3 x^7}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {10 \left (65-64 e^4\right ) \left (1-e^4\right )^2 x^6}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {80 \left (1-e^4\right )^2 x^5}{\left (\left (1-e^4\right ) x^3-4 \left (1-e^4\right ) x^2-1\right )^5}+\frac {64}{\left (\left (1-e^4\right ) x^3-4 \left (1-e^4\right ) x^2-1\right )^5 x^5}+\frac {160 \left (1-e^4\right )^2 x^4}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (e^4-1\right )^5 x^{20}-20 \left (e^4-1\right )^5 x^{19}+160 \left (e^4-1\right )^5 x^{18}-5 \left (e^4-1\right )^4 \left (128 e^4-129\right ) x^{17}+80 \left (e^4-1\right )^4 \left (16 e^4-17\right ) x^{16}-32 \left (e^4-1\right )^4 \left (32 e^4-47\right ) x^{15}-10 \left (e^4-1\right )^3 \left (128 e^4-129\right ) x^{14}+40 \left (e^4-1\right )^3 \left (32 e^4-35\right ) x^{13}+480 \left (e^4-1\right )^3 x^{12}-10 \left (e^4-1\right )^2 \left (64 e^4-65\right ) x^{11}-80 \left (e^4-1\right )^2 x^{10}+160 \left (e^4-1\right )^2 x^9+5 \left (e^4-1\right ) x^8-20 \left (e^4-1\right ) x^7+x^5-256 \left (e^4-1\right ) x^3+768 \left (e^4-1\right ) x^2-64}{x^5 \left (\left (e^4-1\right ) x^3-4 \left (e^4-1\right ) x^2+1\right )^5}dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {\left (e^4-1\right )^5 x^{20}-20 \left (e^4-1\right )^5 x^{19}+160 \left (e^4-1\right )^5 x^{18}-5 \left (e^4-1\right )^4 \left (128 e^4-129\right ) x^{17}+80 \left (e^4-1\right )^4 \left (16 e^4-17\right ) x^{16}-32 \left (e^4-1\right )^4 \left (32 e^4-47\right ) x^{15}-10 \left (e^4-1\right )^3 \left (128 e^4-129\right ) x^{14}+40 \left (e^4-1\right )^3 \left (32 e^4-35\right ) x^{13}+480 \left (e^4-1\right )^3 x^{12}-10 \left (e^4-1\right )^2 \left (64 e^4-65\right ) x^{11}-80 \left (e^4-1\right )^2 x^{10}+160 \left (e^4-1\right )^2 x^9+5 \left (e^4-1\right ) x^8-20 \left (e^4-1\right ) x^7+x^5-256 \left (e^4-1\right ) x^3+768 \left (e^4-1\right ) x^2-64}{x^5 \left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {5 \left (e^4-1\right ) x^3}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {20 \left (1-e^4\right ) x^2}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {1}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {256 \left (1-e^4\right )}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5 x^2}+\frac {768 \left (e^4-1\right )}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5 x^3}+\frac {\left (e^4-1\right )^5 x^{15}}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {20 \left (1-e^4\right )^5 x^{14}}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {160 \left (e^4-1\right )^5 x^{13}}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {5 \left (129-128 e^4\right ) \left (1-e^4\right )^4 x^{12}}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {80 \left (1-e^4\right )^4 \left (16 e^4-17\right ) x^{11}}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {32 \left (47-32 e^4\right ) \left (1-e^4\right )^4 x^{10}}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {10 \left (1-e^4\right )^3 \left (128 e^4-129\right ) x^9}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {40 \left (35-32 e^4\right ) \left (1-e^4\right )^3 x^8}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {480 \left (e^4-1\right )^3 x^7}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {10 \left (65-64 e^4\right ) \left (1-e^4\right )^2 x^6}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {80 \left (1-e^4\right )^2 x^5}{\left (\left (1-e^4\right ) x^3-4 \left (1-e^4\right ) x^2-1\right )^5}+\frac {64}{\left (\left (1-e^4\right ) x^3-4 \left (1-e^4\right ) x^2-1\right )^5 x^5}+\frac {160 \left (1-e^4\right )^2 x^4}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (e^4-1\right )^5 x^{20}-20 \left (e^4-1\right )^5 x^{19}+160 \left (e^4-1\right )^5 x^{18}-5 \left (e^4-1\right )^4 \left (128 e^4-129\right ) x^{17}+80 \left (e^4-1\right )^4 \left (16 e^4-17\right ) x^{16}-32 \left (e^4-1\right )^4 \left (32 e^4-47\right ) x^{15}-10 \left (e^4-1\right )^3 \left (128 e^4-129\right ) x^{14}+40 \left (e^4-1\right )^3 \left (32 e^4-35\right ) x^{13}+480 \left (e^4-1\right )^3 x^{12}-10 \left (e^4-1\right )^2 \left (64 e^4-65\right ) x^{11}-80 \left (e^4-1\right )^2 x^{10}+160 \left (e^4-1\right )^2 x^9+5 \left (e^4-1\right ) x^8-20 \left (e^4-1\right ) x^7+x^5-256 \left (e^4-1\right ) x^3+768 \left (e^4-1\right ) x^2-64}{x^5 \left (\left (e^4-1\right ) x^3-4 \left (e^4-1\right ) x^2+1\right )^5}dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {\left (e^4-1\right )^5 x^{20}-20 \left (e^4-1\right )^5 x^{19}+160 \left (e^4-1\right )^5 x^{18}-5 \left (e^4-1\right )^4 \left (128 e^4-129\right ) x^{17}+80 \left (e^4-1\right )^4 \left (16 e^4-17\right ) x^{16}-32 \left (e^4-1\right )^4 \left (32 e^4-47\right ) x^{15}-10 \left (e^4-1\right )^3 \left (128 e^4-129\right ) x^{14}+40 \left (e^4-1\right )^3 \left (32 e^4-35\right ) x^{13}+480 \left (e^4-1\right )^3 x^{12}-10 \left (e^4-1\right )^2 \left (64 e^4-65\right ) x^{11}-80 \left (e^4-1\right )^2 x^{10}+160 \left (e^4-1\right )^2 x^9+5 \left (e^4-1\right ) x^8-20 \left (e^4-1\right ) x^7+x^5-256 \left (e^4-1\right ) x^3+768 \left (e^4-1\right ) x^2-64}{x^5 \left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {5 \left (e^4-1\right ) x^3}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {20 \left (1-e^4\right ) x^2}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {1}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {256 \left (1-e^4\right )}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5 x^2}+\frac {768 \left (e^4-1\right )}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5 x^3}+\frac {\left (e^4-1\right )^5 x^{15}}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {20 \left (1-e^4\right )^5 x^{14}}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {160 \left (e^4-1\right )^5 x^{13}}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {5 \left (129-128 e^4\right ) \left (1-e^4\right )^4 x^{12}}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {80 \left (1-e^4\right )^4 \left (16 e^4-17\right ) x^{11}}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {32 \left (47-32 e^4\right ) \left (1-e^4\right )^4 x^{10}}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {10 \left (1-e^4\right )^3 \left (128 e^4-129\right ) x^9}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {40 \left (35-32 e^4\right ) \left (1-e^4\right )^3 x^8}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {480 \left (e^4-1\right )^3 x^7}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {10 \left (65-64 e^4\right ) \left (1-e^4\right )^2 x^6}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {80 \left (1-e^4\right )^2 x^5}{\left (\left (1-e^4\right ) x^3-4 \left (1-e^4\right ) x^2-1\right )^5}+\frac {64}{\left (\left (1-e^4\right ) x^3-4 \left (1-e^4\right ) x^2-1\right )^5 x^5}+\frac {160 \left (1-e^4\right )^2 x^4}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (e^4-1\right )^5 x^{20}-20 \left (e^4-1\right )^5 x^{19}+160 \left (e^4-1\right )^5 x^{18}-5 \left (e^4-1\right )^4 \left (128 e^4-129\right ) x^{17}+80 \left (e^4-1\right )^4 \left (16 e^4-17\right ) x^{16}-32 \left (e^4-1\right )^4 \left (32 e^4-47\right ) x^{15}-10 \left (e^4-1\right )^3 \left (128 e^4-129\right ) x^{14}+40 \left (e^4-1\right )^3 \left (32 e^4-35\right ) x^{13}+480 \left (e^4-1\right )^3 x^{12}-10 \left (e^4-1\right )^2 \left (64 e^4-65\right ) x^{11}-80 \left (e^4-1\right )^2 x^{10}+160 \left (e^4-1\right )^2 x^9+5 \left (e^4-1\right ) x^8-20 \left (e^4-1\right ) x^7+x^5-256 \left (e^4-1\right ) x^3+768 \left (e^4-1\right ) x^2-64}{x^5 \left (\left (e^4-1\right ) x^3-4 \left (e^4-1\right ) x^2+1\right )^5}dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {\left (e^4-1\right )^5 x^{20}-20 \left (e^4-1\right )^5 x^{19}+160 \left (e^4-1\right )^5 x^{18}-5 \left (e^4-1\right )^4 \left (128 e^4-129\right ) x^{17}+80 \left (e^4-1\right )^4 \left (16 e^4-17\right ) x^{16}-32 \left (e^4-1\right )^4 \left (32 e^4-47\right ) x^{15}-10 \left (e^4-1\right )^3 \left (128 e^4-129\right ) x^{14}+40 \left (e^4-1\right )^3 \left (32 e^4-35\right ) x^{13}+480 \left (e^4-1\right )^3 x^{12}-10 \left (e^4-1\right )^2 \left (64 e^4-65\right ) x^{11}-80 \left (e^4-1\right )^2 x^{10}+160 \left (e^4-1\right )^2 x^9+5 \left (e^4-1\right ) x^8-20 \left (e^4-1\right ) x^7+x^5-256 \left (e^4-1\right ) x^3+768 \left (e^4-1\right ) x^2-64}{x^5 \left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {5 \left (e^4-1\right ) x^3}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {20 \left (1-e^4\right ) x^2}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {1}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {256 \left (1-e^4\right )}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5 x^2}+\frac {768 \left (e^4-1\right )}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5 x^3}+\frac {\left (e^4-1\right )^5 x^{15}}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {20 \left (1-e^4\right )^5 x^{14}}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {160 \left (e^4-1\right )^5 x^{13}}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {5 \left (129-128 e^4\right ) \left (1-e^4\right )^4 x^{12}}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {80 \left (1-e^4\right )^4 \left (16 e^4-17\right ) x^{11}}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {32 \left (47-32 e^4\right ) \left (1-e^4\right )^4 x^{10}}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {10 \left (1-e^4\right )^3 \left (128 e^4-129\right ) x^9}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {40 \left (35-32 e^4\right ) \left (1-e^4\right )^3 x^8}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {480 \left (e^4-1\right )^3 x^7}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {10 \left (65-64 e^4\right ) \left (1-e^4\right )^2 x^6}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {80 \left (1-e^4\right )^2 x^5}{\left (\left (1-e^4\right ) x^3-4 \left (1-e^4\right ) x^2-1\right )^5}+\frac {64}{\left (\left (1-e^4\right ) x^3-4 \left (1-e^4\right ) x^2-1\right )^5 x^5}+\frac {160 \left (1-e^4\right )^2 x^4}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (e^4-1\right )^5 x^{20}-20 \left (e^4-1\right )^5 x^{19}+160 \left (e^4-1\right )^5 x^{18}-5 \left (e^4-1\right )^4 \left (128 e^4-129\right ) x^{17}+80 \left (e^4-1\right )^4 \left (16 e^4-17\right ) x^{16}-32 \left (e^4-1\right )^4 \left (32 e^4-47\right ) x^{15}-10 \left (e^4-1\right )^3 \left (128 e^4-129\right ) x^{14}+40 \left (e^4-1\right )^3 \left (32 e^4-35\right ) x^{13}+480 \left (e^4-1\right )^3 x^{12}-10 \left (e^4-1\right )^2 \left (64 e^4-65\right ) x^{11}-80 \left (e^4-1\right )^2 x^{10}+160 \left (e^4-1\right )^2 x^9+5 \left (e^4-1\right ) x^8-20 \left (e^4-1\right ) x^7+x^5-256 \left (e^4-1\right ) x^3+768 \left (e^4-1\right ) x^2-64}{x^5 \left (\left (e^4-1\right ) x^3-4 \left (e^4-1\right ) x^2+1\right )^5}dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {\left (e^4-1\right )^5 x^{20}-20 \left (e^4-1\right )^5 x^{19}+160 \left (e^4-1\right )^5 x^{18}-5 \left (e^4-1\right )^4 \left (128 e^4-129\right ) x^{17}+80 \left (e^4-1\right )^4 \left (16 e^4-17\right ) x^{16}-32 \left (e^4-1\right )^4 \left (32 e^4-47\right ) x^{15}-10 \left (e^4-1\right )^3 \left (128 e^4-129\right ) x^{14}+40 \left (e^4-1\right )^3 \left (32 e^4-35\right ) x^{13}+480 \left (e^4-1\right )^3 x^{12}-10 \left (e^4-1\right )^2 \left (64 e^4-65\right ) x^{11}-80 \left (e^4-1\right )^2 x^{10}+160 \left (e^4-1\right )^2 x^9+5 \left (e^4-1\right ) x^8-20 \left (e^4-1\right ) x^7+x^5-256 \left (e^4-1\right ) x^3+768 \left (e^4-1\right ) x^2-64}{x^5 \left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {5 \left (e^4-1\right ) x^3}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {20 \left (1-e^4\right ) x^2}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {1}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {256 \left (1-e^4\right )}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5 x^2}+\frac {768 \left (e^4-1\right )}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5 x^3}+\frac {\left (e^4-1\right )^5 x^{15}}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {20 \left (1-e^4\right )^5 x^{14}}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {160 \left (e^4-1\right )^5 x^{13}}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {5 \left (129-128 e^4\right ) \left (1-e^4\right )^4 x^{12}}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {80 \left (1-e^4\right )^4 \left (16 e^4-17\right ) x^{11}}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {32 \left (47-32 e^4\right ) \left (1-e^4\right )^4 x^{10}}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {10 \left (1-e^4\right )^3 \left (128 e^4-129\right ) x^9}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {40 \left (35-32 e^4\right ) \left (1-e^4\right )^3 x^8}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {480 \left (e^4-1\right )^3 x^7}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {10 \left (65-64 e^4\right ) \left (1-e^4\right )^2 x^6}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {80 \left (1-e^4\right )^2 x^5}{\left (\left (1-e^4\right ) x^3-4 \left (1-e^4\right ) x^2-1\right )^5}+\frac {64}{\left (\left (1-e^4\right ) x^3-4 \left (1-e^4\right ) x^2-1\right )^5 x^5}+\frac {160 \left (1-e^4\right )^2 x^4}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (e^4-1\right )^5 x^{20}-20 \left (e^4-1\right )^5 x^{19}+160 \left (e^4-1\right )^5 x^{18}-5 \left (e^4-1\right )^4 \left (128 e^4-129\right ) x^{17}+80 \left (e^4-1\right )^4 \left (16 e^4-17\right ) x^{16}-32 \left (e^4-1\right )^4 \left (32 e^4-47\right ) x^{15}-10 \left (e^4-1\right )^3 \left (128 e^4-129\right ) x^{14}+40 \left (e^4-1\right )^3 \left (32 e^4-35\right ) x^{13}+480 \left (e^4-1\right )^3 x^{12}-10 \left (e^4-1\right )^2 \left (64 e^4-65\right ) x^{11}-80 \left (e^4-1\right )^2 x^{10}+160 \left (e^4-1\right )^2 x^9+5 \left (e^4-1\right ) x^8-20 \left (e^4-1\right ) x^7+x^5-256 \left (e^4-1\right ) x^3+768 \left (e^4-1\right ) x^2-64}{x^5 \left (\left (e^4-1\right ) x^3-4 \left (e^4-1\right ) x^2+1\right )^5}dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {\left (e^4-1\right )^5 x^{20}-20 \left (e^4-1\right )^5 x^{19}+160 \left (e^4-1\right )^5 x^{18}-5 \left (e^4-1\right )^4 \left (128 e^4-129\right ) x^{17}+80 \left (e^4-1\right )^4 \left (16 e^4-17\right ) x^{16}-32 \left (e^4-1\right )^4 \left (32 e^4-47\right ) x^{15}-10 \left (e^4-1\right )^3 \left (128 e^4-129\right ) x^{14}+40 \left (e^4-1\right )^3 \left (32 e^4-35\right ) x^{13}+480 \left (e^4-1\right )^3 x^{12}-10 \left (e^4-1\right )^2 \left (64 e^4-65\right ) x^{11}-80 \left (e^4-1\right )^2 x^{10}+160 \left (e^4-1\right )^2 x^9+5 \left (e^4-1\right ) x^8-20 \left (e^4-1\right ) x^7+x^5-256 \left (e^4-1\right ) x^3+768 \left (e^4-1\right ) x^2-64}{x^5 \left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {5 \left (e^4-1\right ) x^3}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {20 \left (1-e^4\right ) x^2}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {1}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {256 \left (1-e^4\right )}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5 x^2}+\frac {768 \left (e^4-1\right )}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5 x^3}+\frac {\left (e^4-1\right )^5 x^{15}}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {20 \left (1-e^4\right )^5 x^{14}}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {160 \left (e^4-1\right )^5 x^{13}}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {5 \left (129-128 e^4\right ) \left (1-e^4\right )^4 x^{12}}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {80 \left (1-e^4\right )^4 \left (16 e^4-17\right ) x^{11}}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {32 \left (47-32 e^4\right ) \left (1-e^4\right )^4 x^{10}}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {10 \left (1-e^4\right )^3 \left (128 e^4-129\right ) x^9}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {40 \left (35-32 e^4\right ) \left (1-e^4\right )^3 x^8}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {480 \left (e^4-1\right )^3 x^7}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {10 \left (65-64 e^4\right ) \left (1-e^4\right )^2 x^6}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {80 \left (1-e^4\right )^2 x^5}{\left (\left (1-e^4\right ) x^3-4 \left (1-e^4\right ) x^2-1\right )^5}+\frac {64}{\left (\left (1-e^4\right ) x^3-4 \left (1-e^4\right ) x^2-1\right )^5 x^5}+\frac {160 \left (1-e^4\right )^2 x^4}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (e^4-1\right )^5 x^{20}-20 \left (e^4-1\right )^5 x^{19}+160 \left (e^4-1\right )^5 x^{18}-5 \left (e^4-1\right )^4 \left (128 e^4-129\right ) x^{17}+80 \left (e^4-1\right )^4 \left (16 e^4-17\right ) x^{16}-32 \left (e^4-1\right )^4 \left (32 e^4-47\right ) x^{15}-10 \left (e^4-1\right )^3 \left (128 e^4-129\right ) x^{14}+40 \left (e^4-1\right )^3 \left (32 e^4-35\right ) x^{13}+480 \left (e^4-1\right )^3 x^{12}-10 \left (e^4-1\right )^2 \left (64 e^4-65\right ) x^{11}-80 \left (e^4-1\right )^2 x^{10}+160 \left (e^4-1\right )^2 x^9+5 \left (e^4-1\right ) x^8-20 \left (e^4-1\right ) x^7+x^5-256 \left (e^4-1\right ) x^3+768 \left (e^4-1\right ) x^2-64}{x^5 \left (\left (e^4-1\right ) x^3-4 \left (e^4-1\right ) x^2+1\right )^5}dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {\left (e^4-1\right )^5 x^{20}-20 \left (e^4-1\right )^5 x^{19}+160 \left (e^4-1\right )^5 x^{18}-5 \left (e^4-1\right )^4 \left (128 e^4-129\right ) x^{17}+80 \left (e^4-1\right )^4 \left (16 e^4-17\right ) x^{16}-32 \left (e^4-1\right )^4 \left (32 e^4-47\right ) x^{15}-10 \left (e^4-1\right )^3 \left (128 e^4-129\right ) x^{14}+40 \left (e^4-1\right )^3 \left (32 e^4-35\right ) x^{13}+480 \left (e^4-1\right )^3 x^{12}-10 \left (e^4-1\right )^2 \left (64 e^4-65\right ) x^{11}-80 \left (e^4-1\right )^2 x^{10}+160 \left (e^4-1\right )^2 x^9+5 \left (e^4-1\right ) x^8-20 \left (e^4-1\right ) x^7+x^5-256 \left (e^4-1\right ) x^3+768 \left (e^4-1\right ) x^2-64}{x^5 \left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {5 \left (e^4-1\right ) x^3}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {20 \left (1-e^4\right ) x^2}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {1}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {256 \left (1-e^4\right )}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5 x^2}+\frac {768 \left (e^4-1\right )}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5 x^3}+\frac {\left (e^4-1\right )^5 x^{15}}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {20 \left (1-e^4\right )^5 x^{14}}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {160 \left (e^4-1\right )^5 x^{13}}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {5 \left (129-128 e^4\right ) \left (1-e^4\right )^4 x^{12}}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {80 \left (1-e^4\right )^4 \left (16 e^4-17\right ) x^{11}}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {32 \left (47-32 e^4\right ) \left (1-e^4\right )^4 x^{10}}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {10 \left (1-e^4\right )^3 \left (128 e^4-129\right ) x^9}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {40 \left (35-32 e^4\right ) \left (1-e^4\right )^3 x^8}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {480 \left (e^4-1\right )^3 x^7}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {10 \left (65-64 e^4\right ) \left (1-e^4\right )^2 x^6}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {80 \left (1-e^4\right )^2 x^5}{\left (\left (1-e^4\right ) x^3-4 \left (1-e^4\right ) x^2-1\right )^5}+\frac {64}{\left (\left (1-e^4\right ) x^3-4 \left (1-e^4\right ) x^2-1\right )^5 x^5}+\frac {160 \left (1-e^4\right )^2 x^4}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (e^4-1\right )^5 x^{20}-20 \left (e^4-1\right )^5 x^{19}+160 \left (e^4-1\right )^5 x^{18}-5 \left (e^4-1\right )^4 \left (128 e^4-129\right ) x^{17}+80 \left (e^4-1\right )^4 \left (16 e^4-17\right ) x^{16}-32 \left (e^4-1\right )^4 \left (32 e^4-47\right ) x^{15}-10 \left (e^4-1\right )^3 \left (128 e^4-129\right ) x^{14}+40 \left (e^4-1\right )^3 \left (32 e^4-35\right ) x^{13}+480 \left (e^4-1\right )^3 x^{12}-10 \left (e^4-1\right )^2 \left (64 e^4-65\right ) x^{11}-80 \left (e^4-1\right )^2 x^{10}+160 \left (e^4-1\right )^2 x^9+5 \left (e^4-1\right ) x^8-20 \left (e^4-1\right ) x^7+x^5-256 \left (e^4-1\right ) x^3+768 \left (e^4-1\right ) x^2-64}{x^5 \left (\left (e^4-1\right ) x^3-4 \left (e^4-1\right ) x^2+1\right )^5}dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {\left (e^4-1\right )^5 x^{20}-20 \left (e^4-1\right )^5 x^{19}+160 \left (e^4-1\right )^5 x^{18}-5 \left (e^4-1\right )^4 \left (128 e^4-129\right ) x^{17}+80 \left (e^4-1\right )^4 \left (16 e^4-17\right ) x^{16}-32 \left (e^4-1\right )^4 \left (32 e^4-47\right ) x^{15}-10 \left (e^4-1\right )^3 \left (128 e^4-129\right ) x^{14}+40 \left (e^4-1\right )^3 \left (32 e^4-35\right ) x^{13}+480 \left (e^4-1\right )^3 x^{12}-10 \left (e^4-1\right )^2 \left (64 e^4-65\right ) x^{11}-80 \left (e^4-1\right )^2 x^{10}+160 \left (e^4-1\right )^2 x^9+5 \left (e^4-1\right ) x^8-20 \left (e^4-1\right ) x^7+x^5-256 \left (e^4-1\right ) x^3+768 \left (e^4-1\right ) x^2-64}{x^5 \left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {5 \left (e^4-1\right ) x^3}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {20 \left (1-e^4\right ) x^2}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {1}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {256 \left (1-e^4\right )}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5 x^2}+\frac {768 \left (e^4-1\right )}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5 x^3}+\frac {\left (e^4-1\right )^5 x^{15}}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {20 \left (1-e^4\right )^5 x^{14}}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {160 \left (e^4-1\right )^5 x^{13}}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {5 \left (129-128 e^4\right ) \left (1-e^4\right )^4 x^{12}}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {80 \left (1-e^4\right )^4 \left (16 e^4-17\right ) x^{11}}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {32 \left (47-32 e^4\right ) \left (1-e^4\right )^4 x^{10}}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {10 \left (1-e^4\right )^3 \left (128 e^4-129\right ) x^9}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {40 \left (35-32 e^4\right ) \left (1-e^4\right )^3 x^8}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {480 \left (e^4-1\right )^3 x^7}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {10 \left (65-64 e^4\right ) \left (1-e^4\right )^2 x^6}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {80 \left (1-e^4\right )^2 x^5}{\left (\left (1-e^4\right ) x^3-4 \left (1-e^4\right ) x^2-1\right )^5}+\frac {64}{\left (\left (1-e^4\right ) x^3-4 \left (1-e^4\right ) x^2-1\right )^5 x^5}+\frac {160 \left (1-e^4\right )^2 x^4}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (e^4-1\right )^5 x^{20}-20 \left (e^4-1\right )^5 x^{19}+160 \left (e^4-1\right )^5 x^{18}-5 \left (e^4-1\right )^4 \left (128 e^4-129\right ) x^{17}+80 \left (e^4-1\right )^4 \left (16 e^4-17\right ) x^{16}-32 \left (e^4-1\right )^4 \left (32 e^4-47\right ) x^{15}-10 \left (e^4-1\right )^3 \left (128 e^4-129\right ) x^{14}+40 \left (e^4-1\right )^3 \left (32 e^4-35\right ) x^{13}+480 \left (e^4-1\right )^3 x^{12}-10 \left (e^4-1\right )^2 \left (64 e^4-65\right ) x^{11}-80 \left (e^4-1\right )^2 x^{10}+160 \left (e^4-1\right )^2 x^9+5 \left (e^4-1\right ) x^8-20 \left (e^4-1\right ) x^7+x^5-256 \left (e^4-1\right ) x^3+768 \left (e^4-1\right ) x^2-64}{x^5 \left (\left (e^4-1\right ) x^3-4 \left (e^4-1\right ) x^2+1\right )^5}dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {\left (e^4-1\right )^5 x^{20}-20 \left (e^4-1\right )^5 x^{19}+160 \left (e^4-1\right )^5 x^{18}-5 \left (e^4-1\right )^4 \left (128 e^4-129\right ) x^{17}+80 \left (e^4-1\right )^4 \left (16 e^4-17\right ) x^{16}-32 \left (e^4-1\right )^4 \left (32 e^4-47\right ) x^{15}-10 \left (e^4-1\right )^3 \left (128 e^4-129\right ) x^{14}+40 \left (e^4-1\right )^3 \left (32 e^4-35\right ) x^{13}+480 \left (e^4-1\right )^3 x^{12}-10 \left (e^4-1\right )^2 \left (64 e^4-65\right ) x^{11}-80 \left (e^4-1\right )^2 x^{10}+160 \left (e^4-1\right )^2 x^9+5 \left (e^4-1\right ) x^8-20 \left (e^4-1\right ) x^7+x^5-256 \left (e^4-1\right ) x^3+768 \left (e^4-1\right ) x^2-64}{x^5 \left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {5 \left (e^4-1\right ) x^3}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {20 \left (1-e^4\right ) x^2}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {1}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {256 \left (1-e^4\right )}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5 x^2}+\frac {768 \left (e^4-1\right )}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5 x^3}+\frac {\left (e^4-1\right )^5 x^{15}}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {20 \left (1-e^4\right )^5 x^{14}}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {160 \left (e^4-1\right )^5 x^{13}}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {5 \left (129-128 e^4\right ) \left (1-e^4\right )^4 x^{12}}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {80 \left (1-e^4\right )^4 \left (16 e^4-17\right ) x^{11}}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {32 \left (47-32 e^4\right ) \left (1-e^4\right )^4 x^{10}}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {10 \left (1-e^4\right )^3 \left (128 e^4-129\right ) x^9}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {40 \left (35-32 e^4\right ) \left (1-e^4\right )^3 x^8}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {480 \left (e^4-1\right )^3 x^7}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {10 \left (65-64 e^4\right ) \left (1-e^4\right )^2 x^6}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}+\frac {80 \left (1-e^4\right )^2 x^5}{\left (\left (1-e^4\right ) x^3-4 \left (1-e^4\right ) x^2-1\right )^5}+\frac {64}{\left (\left (1-e^4\right ) x^3-4 \left (1-e^4\right ) x^2-1\right )^5 x^5}+\frac {160 \left (1-e^4\right )^2 x^4}{\left (-\left (\left (1-e^4\right ) x^3\right )+4 \left (1-e^4\right ) x^2+1\right )^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\left (e^4-1\right )^5 x^{20}-20 \left (e^4-1\right )^5 x^{19}+160 \left (e^4-1\right )^5 x^{18}-5 \left (e^4-1\right )^4 \left (128 e^4-129\right ) x^{17}+80 \left (e^4-1\right )^4 \left (16 e^4-17\right ) x^{16}-32 \left (e^4-1\right )^4 \left (32 e^4-47\right ) x^{15}-10 \left (e^4-1\right )^3 \left (128 e^4-129\right ) x^{14}+40 \left (e^4-1\right )^3 \left (32 e^4-35\right ) x^{13}+480 \left (e^4-1\right )^3 x^{12}-10 \left (e^4-1\right )^2 \left (64 e^4-65\right ) x^{11}-80 \left (e^4-1\right )^2 x^{10}+160 \left (e^4-1\right )^2 x^9+5 \left (e^4-1\right ) x^8-20 \left (e^4-1\right ) x^7+x^5-256 \left (e^4-1\right ) x^3+768 \left (e^4-1\right ) x^2-64}{x^5 \left (\left (e^4-1\right ) x^3-4 \left (e^4-1\right ) x^2+1\right )^5}dx\) |
Int[(-64 - 768*x^2 + 256*x^3 + x^5 + 20*x^7 - 5*x^8 + 160*x^9 - 80*x^10 + 650*x^11 - 480*x^12 + 1400*x^13 - 1290*x^14 + 1504*x^15 - 1360*x^16 + 645* x^17 - 160*x^18 + 20*x^19 - x^20 + E^8*(160*x^9 - 80*x^10 + 1930*x^11 - 14 40*x^12 + 8040*x^13 - 7710*x^14 + 13120*x^15 - 13280*x^16 + 6430*x^17 - 16 00*x^18 + 200*x^19 - 10*x^20) + E^16*(1280*x^13 - 1280*x^14 + 5600*x^15 - 6480*x^16 + 3205*x^17 - 800*x^18 + 100*x^19 - 5*x^20) + E^20*(-1024*x^15 + 1280*x^16 - 640*x^17 + 160*x^18 - 20*x^19 + x^20) + E^4*(768*x^2 - 256*x^ 3 - 20*x^7 + 5*x^8 - 320*x^9 + 160*x^10 - 1940*x^11 + 1440*x^12 - 5480*x^1 3 + 5150*x^14 - 7040*x^15 + 6720*x^16 - 3220*x^17 + 800*x^18 - 100*x^19 + 5*x^20) + E^12*(-640*x^11 + 480*x^12 - 5240*x^13 + 5130*x^14 - 12160*x^15 + 13120*x^16 - 6420*x^17 + 1600*x^18 - 200*x^19 + 10*x^20))/(x^5 + 20*x^7 - 5*x^8 + 160*x^9 - 80*x^10 + 650*x^11 - 480*x^12 + 1400*x^13 - 1290*x^14 + 1504*x^15 - 1360*x^16 + 645*x^17 - 160*x^18 + 20*x^19 - x^20 + E^8*(160* x^9 - 80*x^10 + 1930*x^11 - 1440*x^12 + 8040*x^13 - 7710*x^14 + 13120*x^15 - 13280*x^16 + 6430*x^17 - 1600*x^18 + 200*x^19 - 10*x^20) + E^16*(1280*x ^13 - 1280*x^14 + 5600*x^15 - 6480*x^16 + 3205*x^17 - 800*x^18 + 100*x^19 - 5*x^20) + E^20*(-1024*x^15 + 1280*x^16 - 640*x^17 + 160*x^18 - 20*x^19 + x^20) + E^4*(-20*x^7 + 5*x^8 - 320*x^9 + 160*x^10 - 1940*x^11 + 1440*x^12 - 5480*x^13 + 5150*x^14 - 7040*x^15 + 6720*x^16 - 3220*x^17 + 800*x^18 - 100*x^19 + 5*x^20) + E^12*(-640*x^11 + 480*x^12 - 5240*x^13 + 5130*x^14 - 12160*x^15 + 13120*x^16 - 6420*x^17 + 1600*x^18 - 200*x^19 + 10*x^20)),x]
3.9.86.3.1 Defintions of rubi rules used
Int[(Fx_.)*(Px_)^(p_.), x_Symbol] :> With[{r = Expon[Px, x, Min]}, Int[x^(p *r)*ExpandToSum[Px/x^r, x]^p*Fx, x] /; IGtQ[r, 0]] /; PolyQ[Px, x] && Integ erQ[p] && !MonomialQ[Px, x] && (ILtQ[p, 0] || !PolyQ[u, x])
Int[(u_.)*(Px_)^(p_), x_Symbol] :> With[{Qx = Factor[Px]}, Int[ExpandIntegr and[u*Qx^p, x], x] /; !SumQ[NonfreeFactors[Qx, x]]] /; PolyQ[Px, x] && GtQ [Expon[Px, x], 2] && !BinomialQ[Px, x] && !TrinomialQ[Px, x] && ILtQ[p, 0 ] && RationalFunctionQ[u, x]
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl erIntegrandQ[v, u, x]]
Timed out.
\[\int \frac {\left (x^{20}-20 x^{19}+160 x^{18}-640 x^{17}+1280 x^{16}-1024 x^{15}\right ) {\mathrm e}^{20}+\left (-5 x^{20}+100 x^{19}-800 x^{18}+3205 x^{17}-6480 x^{16}+5600 x^{15}-1280 x^{14}+1280 x^{13}\right ) {\mathrm e}^{16}+\left (10 x^{20}-200 x^{19}+1600 x^{18}-6420 x^{17}+13120 x^{16}-12160 x^{15}+5130 x^{14}-5240 x^{13}+480 x^{12}-640 x^{11}\right ) {\mathrm e}^{12}+\left (-10 x^{20}+200 x^{19}-1600 x^{18}+6430 x^{17}-13280 x^{16}+13120 x^{15}-7710 x^{14}+8040 x^{13}-1440 x^{12}+1930 x^{11}-80 x^{10}+160 x^{9}\right ) {\mathrm e}^{8}+\left (5 x^{20}-100 x^{19}+800 x^{18}-3220 x^{17}+6720 x^{16}-7040 x^{15}+5150 x^{14}-5480 x^{13}+1440 x^{12}-1940 x^{11}+160 x^{10}-320 x^{9}+5 x^{8}-20 x^{7}-256 x^{3}+768 x^{2}\right ) {\mathrm e}^{4}-x^{20}+20 x^{19}-160 x^{18}+645 x^{17}-1360 x^{16}+1504 x^{15}-1290 x^{14}+1400 x^{13}-480 x^{12}+650 x^{11}-80 x^{10}+160 x^{9}-5 x^{8}+20 x^{7}+x^{5}+256 x^{3}-768 x^{2}-64}{\left (x^{20}-20 x^{19}+160 x^{18}-640 x^{17}+1280 x^{16}-1024 x^{15}\right ) {\mathrm e}^{20}+\left (-5 x^{20}+100 x^{19}-800 x^{18}+3205 x^{17}-6480 x^{16}+5600 x^{15}-1280 x^{14}+1280 x^{13}\right ) {\mathrm e}^{16}+\left (10 x^{20}-200 x^{19}+1600 x^{18}-6420 x^{17}+13120 x^{16}-12160 x^{15}+5130 x^{14}-5240 x^{13}+480 x^{12}-640 x^{11}\right ) {\mathrm e}^{12}+\left (-10 x^{20}+200 x^{19}-1600 x^{18}+6430 x^{17}-13280 x^{16}+13120 x^{15}-7710 x^{14}+8040 x^{13}-1440 x^{12}+1930 x^{11}-80 x^{10}+160 x^{9}\right ) {\mathrm e}^{8}+\left (5 x^{20}-100 x^{19}+800 x^{18}-3220 x^{17}+6720 x^{16}-7040 x^{15}+5150 x^{14}-5480 x^{13}+1440 x^{12}-1940 x^{11}+160 x^{10}-320 x^{9}+5 x^{8}-20 x^{7}\right ) {\mathrm e}^{4}-x^{20}+20 x^{19}-160 x^{18}+645 x^{17}-1360 x^{16}+1504 x^{15}-1290 x^{14}+1400 x^{13}-480 x^{12}+650 x^{11}-80 x^{10}+160 x^{9}-5 x^{8}+20 x^{7}+x^{5}}d x\]
int(((x^20-20*x^19+160*x^18-640*x^17+1280*x^16-1024*x^15)*exp(4)^5+(-5*x^2 0+100*x^19-800*x^18+3205*x^17-6480*x^16+5600*x^15-1280*x^14+1280*x^13)*exp (4)^4+(10*x^20-200*x^19+1600*x^18-6420*x^17+13120*x^16-12160*x^15+5130*x^1 4-5240*x^13+480*x^12-640*x^11)*exp(4)^3+(-10*x^20+200*x^19-1600*x^18+6430* x^17-13280*x^16+13120*x^15-7710*x^14+8040*x^13-1440*x^12+1930*x^11-80*x^10 +160*x^9)*exp(4)^2+(5*x^20-100*x^19+800*x^18-3220*x^17+6720*x^16-7040*x^15 +5150*x^14-5480*x^13+1440*x^12-1940*x^11+160*x^10-320*x^9+5*x^8-20*x^7-256 *x^3+768*x^2)*exp(4)-x^20+20*x^19-160*x^18+645*x^17-1360*x^16+1504*x^15-12 90*x^14+1400*x^13-480*x^12+650*x^11-80*x^10+160*x^9-5*x^8+20*x^7+x^5+256*x ^3-768*x^2-64)/((x^20-20*x^19+160*x^18-640*x^17+1280*x^16-1024*x^15)*exp(4 )^5+(-5*x^20+100*x^19-800*x^18+3205*x^17-6480*x^16+5600*x^15-1280*x^14+128 0*x^13)*exp(4)^4+(10*x^20-200*x^19+1600*x^18-6420*x^17+13120*x^16-12160*x^ 15+5130*x^14-5240*x^13+480*x^12-640*x^11)*exp(4)^3+(-10*x^20+200*x^19-1600 *x^18+6430*x^17-13280*x^16+13120*x^15-7710*x^14+8040*x^13-1440*x^12+1930*x ^11-80*x^10+160*x^9)*exp(4)^2+(5*x^20-100*x^19+800*x^18-3220*x^17+6720*x^1 6-7040*x^15+5150*x^14-5480*x^13+1440*x^12-1940*x^11+160*x^10-320*x^9+5*x^8 -20*x^7)*exp(4)-x^20+20*x^19-160*x^18+645*x^17-1360*x^16+1504*x^15-1290*x^ 14+1400*x^13-480*x^12+650*x^11-80*x^10+160*x^9-5*x^8+20*x^7+x^5),x)
int(((x^20-20*x^19+160*x^18-640*x^17+1280*x^16-1024*x^15)*exp(4)^5+(-5*x^2 0+100*x^19-800*x^18+3205*x^17-6480*x^16+5600*x^15-1280*x^14+1280*x^13)*exp (4)^4+(10*x^20-200*x^19+1600*x^18-6420*x^17+13120*x^16-12160*x^15+5130*x^1 4-5240*x^13+480*x^12-640*x^11)*exp(4)^3+(-10*x^20+200*x^19-1600*x^18+6430* x^17-13280*x^16+13120*x^15-7710*x^14+8040*x^13-1440*x^12+1930*x^11-80*x^10 +160*x^9)*exp(4)^2+(5*x^20-100*x^19+800*x^18-3220*x^17+6720*x^16-7040*x^15 +5150*x^14-5480*x^13+1440*x^12-1940*x^11+160*x^10-320*x^9+5*x^8-20*x^7-256 *x^3+768*x^2)*exp(4)-x^20+20*x^19-160*x^18+645*x^17-1360*x^16+1504*x^15-12 90*x^14+1400*x^13-480*x^12+650*x^11-80*x^10+160*x^9-5*x^8+20*x^7+x^5+256*x ^3-768*x^2-64)/((x^20-20*x^19+160*x^18-640*x^17+1280*x^16-1024*x^15)*exp(4 )^5+(-5*x^20+100*x^19-800*x^18+3205*x^17-6480*x^16+5600*x^15-1280*x^14+128 0*x^13)*exp(4)^4+(10*x^20-200*x^19+1600*x^18-6420*x^17+13120*x^16-12160*x^ 15+5130*x^14-5240*x^13+480*x^12-640*x^11)*exp(4)^3+(-10*x^20+200*x^19-1600 *x^18+6430*x^17-13280*x^16+13120*x^15-7710*x^14+8040*x^13-1440*x^12+1930*x ^11-80*x^10+160*x^9)*exp(4)^2+(5*x^20-100*x^19+800*x^18-3220*x^17+6720*x^1 6-7040*x^15+5150*x^14-5480*x^13+1440*x^12-1940*x^11+160*x^10-320*x^9+5*x^8 -20*x^7)*exp(4)-x^20+20*x^19-160*x^18+645*x^17-1360*x^16+1504*x^15-1290*x^ 14+1400*x^13-480*x^12+650*x^11-80*x^10+160*x^9-5*x^8+20*x^7+x^5),x)
Leaf count of result is larger than twice the leaf count of optimal. 460 vs. \(2 (23) = 46\).
Time = 0.30 (sec) , antiderivative size = 460, normalized size of antiderivative = 19.17 \[ \int \frac {-64-768 x^2+256 x^3+x^5+20 x^7-5 x^8+160 x^9-80 x^{10}+650 x^{11}-480 x^{12}+1400 x^{13}-1290 x^{14}+1504 x^{15}-1360 x^{16}+645 x^{17}-160 x^{18}+20 x^{19}-x^{20}+e^8 \left (160 x^9-80 x^{10}+1930 x^{11}-1440 x^{12}+8040 x^{13}-7710 x^{14}+13120 x^{15}-13280 x^{16}+6430 x^{17}-1600 x^{18}+200 x^{19}-10 x^{20}\right )+e^{16} \left (1280 x^{13}-1280 x^{14}+5600 x^{15}-6480 x^{16}+3205 x^{17}-800 x^{18}+100 x^{19}-5 x^{20}\right )+e^{20} \left (-1024 x^{15}+1280 x^{16}-640 x^{17}+160 x^{18}-20 x^{19}+x^{20}\right )+e^4 \left (768 x^2-256 x^3-20 x^7+5 x^8-320 x^9+160 x^{10}-1940 x^{11}+1440 x^{12}-5480 x^{13}+5150 x^{14}-7040 x^{15}+6720 x^{16}-3220 x^{17}+800 x^{18}-100 x^{19}+5 x^{20}\right )+e^{12} \left (-640 x^{11}+480 x^{12}-5240 x^{13}+5130 x^{14}-12160 x^{15}+13120 x^{16}-6420 x^{17}+1600 x^{18}-200 x^{19}+10 x^{20}\right )}{x^5+20 x^7-5 x^8+160 x^9-80 x^{10}+650 x^{11}-480 x^{12}+1400 x^{13}-1290 x^{14}+1504 x^{15}-1360 x^{16}+645 x^{17}-160 x^{18}+20 x^{19}-x^{20}+e^8 \left (160 x^9-80 x^{10}+1930 x^{11}-1440 x^{12}+8040 x^{13}-7710 x^{14}+13120 x^{15}-13280 x^{16}+6430 x^{17}-1600 x^{18}+200 x^{19}-10 x^{20}\right )+e^{16} \left (1280 x^{13}-1280 x^{14}+5600 x^{15}-6480 x^{16}+3205 x^{17}-800 x^{18}+100 x^{19}-5 x^{20}\right )+e^{20} \left (-1024 x^{15}+1280 x^{16}-640 x^{17}+160 x^{18}-20 x^{19}+x^{20}\right )+e^4 \left (-20 x^7+5 x^8-320 x^9+160 x^{10}-1940 x^{11}+1440 x^{12}-5480 x^{13}+5150 x^{14}-7040 x^{15}+6720 x^{16}-3220 x^{17}+800 x^{18}-100 x^{19}+5 x^{20}\right )+e^{12} \left (-640 x^{11}+480 x^{12}-5240 x^{13}+5130 x^{14}-12160 x^{15}+13120 x^{16}-6420 x^{17}+1600 x^{18}-200 x^{19}+10 x^{20}\right )} \, dx=\frac {x^{17} - 16 \, x^{16} + 96 \, x^{15} - 260 \, x^{14} + 304 \, x^{13} - 192 \, x^{12} + 262 \, x^{11} - 48 \, x^{10} + 96 \, x^{9} - 4 \, x^{8} + 16 \, x^{7} + x^{5} + {\left (x^{17} - 16 \, x^{16} + 96 \, x^{15} - 256 \, x^{14} + 256 \, x^{13}\right )} e^{16} - 4 \, {\left (x^{17} - 16 \, x^{16} + 96 \, x^{15} - 257 \, x^{14} + 268 \, x^{13} - 48 \, x^{12} + 64 \, x^{11}\right )} e^{12} + 6 \, {\left (x^{17} - 16 \, x^{16} + 96 \, x^{15} - 258 \, x^{14} + 280 \, x^{13} - 96 \, x^{12} + 129 \, x^{11} - 8 \, x^{10} + 16 \, x^{9}\right )} e^{8} - 4 \, {\left (x^{17} - 16 \, x^{16} + 96 \, x^{15} - 259 \, x^{14} + 292 \, x^{13} - 144 \, x^{12} + 195 \, x^{11} - 24 \, x^{10} + 48 \, x^{9} - x^{8} + 4 \, x^{7}\right )} e^{4} + 16}{x^{16} - 16 \, x^{15} + 96 \, x^{14} - 260 \, x^{13} + 304 \, x^{12} - 192 \, x^{11} + 262 \, x^{10} - 48 \, x^{9} + 96 \, x^{8} - 4 \, x^{7} + 16 \, x^{6} + x^{4} + {\left (x^{16} - 16 \, x^{15} + 96 \, x^{14} - 256 \, x^{13} + 256 \, x^{12}\right )} e^{16} - 4 \, {\left (x^{16} - 16 \, x^{15} + 96 \, x^{14} - 257 \, x^{13} + 268 \, x^{12} - 48 \, x^{11} + 64 \, x^{10}\right )} e^{12} + 6 \, {\left (x^{16} - 16 \, x^{15} + 96 \, x^{14} - 258 \, x^{13} + 280 \, x^{12} - 96 \, x^{11} + 129 \, x^{10} - 8 \, x^{9} + 16 \, x^{8}\right )} e^{8} - 4 \, {\left (x^{16} - 16 \, x^{15} + 96 \, x^{14} - 259 \, x^{13} + 292 \, x^{12} - 144 \, x^{11} + 195 \, x^{10} - 24 \, x^{9} + 48 \, x^{8} - x^{7} + 4 \, x^{6}\right )} e^{4}} \]
integrate(((x^20-20*x^19+160*x^18-640*x^17+1280*x^16-1024*x^15)*exp(4)^5+( -5*x^20+100*x^19-800*x^18+3205*x^17-6480*x^16+5600*x^15-1280*x^14+1280*x^1 3)*exp(4)^4+(10*x^20-200*x^19+1600*x^18-6420*x^17+13120*x^16-12160*x^15+51 30*x^14-5240*x^13+480*x^12-640*x^11)*exp(4)^3+(-10*x^20+200*x^19-1600*x^18 +6430*x^17-13280*x^16+13120*x^15-7710*x^14+8040*x^13-1440*x^12+1930*x^11-8 0*x^10+160*x^9)*exp(4)^2+(5*x^20-100*x^19+800*x^18-3220*x^17+6720*x^16-704 0*x^15+5150*x^14-5480*x^13+1440*x^12-1940*x^11+160*x^10-320*x^9+5*x^8-20*x ^7-256*x^3+768*x^2)*exp(4)-x^20+20*x^19-160*x^18+645*x^17-1360*x^16+1504*x ^15-1290*x^14+1400*x^13-480*x^12+650*x^11-80*x^10+160*x^9-5*x^8+20*x^7+x^5 +256*x^3-768*x^2-64)/((x^20-20*x^19+160*x^18-640*x^17+1280*x^16-1024*x^15) *exp(4)^5+(-5*x^20+100*x^19-800*x^18+3205*x^17-6480*x^16+5600*x^15-1280*x^ 14+1280*x^13)*exp(4)^4+(10*x^20-200*x^19+1600*x^18-6420*x^17+13120*x^16-12 160*x^15+5130*x^14-5240*x^13+480*x^12-640*x^11)*exp(4)^3+(-10*x^20+200*x^1 9-1600*x^18+6430*x^17-13280*x^16+13120*x^15-7710*x^14+8040*x^13-1440*x^12+ 1930*x^11-80*x^10+160*x^9)*exp(4)^2+(5*x^20-100*x^19+800*x^18-3220*x^17+67 20*x^16-7040*x^15+5150*x^14-5480*x^13+1440*x^12-1940*x^11+160*x^10-320*x^9 +5*x^8-20*x^7)*exp(4)-x^20+20*x^19-160*x^18+645*x^17-1360*x^16+1504*x^15-1 290*x^14+1400*x^13-480*x^12+650*x^11-80*x^10+160*x^9-5*x^8+20*x^7+x^5),x, algorithm=\
(x^17 - 16*x^16 + 96*x^15 - 260*x^14 + 304*x^13 - 192*x^12 + 262*x^11 - 48 *x^10 + 96*x^9 - 4*x^8 + 16*x^7 + x^5 + (x^17 - 16*x^16 + 96*x^15 - 256*x^ 14 + 256*x^13)*e^16 - 4*(x^17 - 16*x^16 + 96*x^15 - 257*x^14 + 268*x^13 - 48*x^12 + 64*x^11)*e^12 + 6*(x^17 - 16*x^16 + 96*x^15 - 258*x^14 + 280*x^1 3 - 96*x^12 + 129*x^11 - 8*x^10 + 16*x^9)*e^8 - 4*(x^17 - 16*x^16 + 96*x^1 5 - 259*x^14 + 292*x^13 - 144*x^12 + 195*x^11 - 24*x^10 + 48*x^9 - x^8 + 4 *x^7)*e^4 + 16)/(x^16 - 16*x^15 + 96*x^14 - 260*x^13 + 304*x^12 - 192*x^11 + 262*x^10 - 48*x^9 + 96*x^8 - 4*x^7 + 16*x^6 + x^4 + (x^16 - 16*x^15 + 9 6*x^14 - 256*x^13 + 256*x^12)*e^16 - 4*(x^16 - 16*x^15 + 96*x^14 - 257*x^1 3 + 268*x^12 - 48*x^11 + 64*x^10)*e^12 + 6*(x^16 - 16*x^15 + 96*x^14 - 258 *x^13 + 280*x^12 - 96*x^11 + 129*x^10 - 8*x^9 + 16*x^8)*e^8 - 4*(x^16 - 16 *x^15 + 96*x^14 - 259*x^13 + 292*x^12 - 144*x^11 + 195*x^10 - 24*x^9 + 48* x^8 - x^7 + 4*x^6)*e^4)
Leaf count of result is larger than twice the leaf count of optimal. 223 vs. \(2 (19) = 38\).
Time = 58.81 (sec) , antiderivative size = 223, normalized size of antiderivative = 9.29 \[ \int \frac {-64-768 x^2+256 x^3+x^5+20 x^7-5 x^8+160 x^9-80 x^{10}+650 x^{11}-480 x^{12}+1400 x^{13}-1290 x^{14}+1504 x^{15}-1360 x^{16}+645 x^{17}-160 x^{18}+20 x^{19}-x^{20}+e^8 \left (160 x^9-80 x^{10}+1930 x^{11}-1440 x^{12}+8040 x^{13}-7710 x^{14}+13120 x^{15}-13280 x^{16}+6430 x^{17}-1600 x^{18}+200 x^{19}-10 x^{20}\right )+e^{16} \left (1280 x^{13}-1280 x^{14}+5600 x^{15}-6480 x^{16}+3205 x^{17}-800 x^{18}+100 x^{19}-5 x^{20}\right )+e^{20} \left (-1024 x^{15}+1280 x^{16}-640 x^{17}+160 x^{18}-20 x^{19}+x^{20}\right )+e^4 \left (768 x^2-256 x^3-20 x^7+5 x^8-320 x^9+160 x^{10}-1940 x^{11}+1440 x^{12}-5480 x^{13}+5150 x^{14}-7040 x^{15}+6720 x^{16}-3220 x^{17}+800 x^{18}-100 x^{19}+5 x^{20}\right )+e^{12} \left (-640 x^{11}+480 x^{12}-5240 x^{13}+5130 x^{14}-12160 x^{15}+13120 x^{16}-6420 x^{17}+1600 x^{18}-200 x^{19}+10 x^{20}\right )}{x^5+20 x^7-5 x^8+160 x^9-80 x^{10}+650 x^{11}-480 x^{12}+1400 x^{13}-1290 x^{14}+1504 x^{15}-1360 x^{16}+645 x^{17}-160 x^{18}+20 x^{19}-x^{20}+e^8 \left (160 x^9-80 x^{10}+1930 x^{11}-1440 x^{12}+8040 x^{13}-7710 x^{14}+13120 x^{15}-13280 x^{16}+6430 x^{17}-1600 x^{18}+200 x^{19}-10 x^{20}\right )+e^{16} \left (1280 x^{13}-1280 x^{14}+5600 x^{15}-6480 x^{16}+3205 x^{17}-800 x^{18}+100 x^{19}-5 x^{20}\right )+e^{20} \left (-1024 x^{15}+1280 x^{16}-640 x^{17}+160 x^{18}-20 x^{19}+x^{20}\right )+e^4 \left (-20 x^7+5 x^8-320 x^9+160 x^{10}-1940 x^{11}+1440 x^{12}-5480 x^{13}+5150 x^{14}-7040 x^{15}+6720 x^{16}-3220 x^{17}+800 x^{18}-100 x^{19}+5 x^{20}\right )+e^{12} \left (-640 x^{11}+480 x^{12}-5240 x^{13}+5130 x^{14}-12160 x^{15}+13120 x^{16}-6420 x^{17}+1600 x^{18}-200 x^{19}+10 x^{20}\right )} \, dx=x + \frac {16}{x^{16} \left (- 4 e^{12} - 4 e^{4} + 1 + 6 e^{8} + e^{16}\right ) + x^{15} \left (- 16 e^{16} - 96 e^{8} - 16 + 64 e^{4} + 64 e^{12}\right ) + x^{14} \left (- 384 e^{12} - 384 e^{4} + 96 + 576 e^{8} + 96 e^{16}\right ) + x^{13} \left (- 256 e^{16} - 1548 e^{8} - 260 + 1036 e^{4} + 1028 e^{12}\right ) + x^{12} \left (- 1072 e^{12} - 1168 e^{4} + 304 + 1680 e^{8} + 256 e^{16}\right ) + x^{11} \left (- 576 e^{8} - 192 + 576 e^{4} + 192 e^{12}\right ) + x^{10} \left (- 256 e^{12} - 780 e^{4} + 262 + 774 e^{8}\right ) + x^{9} \left (- 48 e^{8} - 48 + 96 e^{4}\right ) + x^{8} \left (- 192 e^{4} + 96 + 96 e^{8}\right ) + x^{7} \left (-4 + 4 e^{4}\right ) + x^{6} \cdot \left (16 - 16 e^{4}\right ) + x^{4}} \]
integrate(((x**20-20*x**19+160*x**18-640*x**17+1280*x**16-1024*x**15)*exp( 4)**5+(-5*x**20+100*x**19-800*x**18+3205*x**17-6480*x**16+5600*x**15-1280* x**14+1280*x**13)*exp(4)**4+(10*x**20-200*x**19+1600*x**18-6420*x**17+1312 0*x**16-12160*x**15+5130*x**14-5240*x**13+480*x**12-640*x**11)*exp(4)**3+( -10*x**20+200*x**19-1600*x**18+6430*x**17-13280*x**16+13120*x**15-7710*x** 14+8040*x**13-1440*x**12+1930*x**11-80*x**10+160*x**9)*exp(4)**2+(5*x**20- 100*x**19+800*x**18-3220*x**17+6720*x**16-7040*x**15+5150*x**14-5480*x**13 +1440*x**12-1940*x**11+160*x**10-320*x**9+5*x**8-20*x**7-256*x**3+768*x**2 )*exp(4)-x**20+20*x**19-160*x**18+645*x**17-1360*x**16+1504*x**15-1290*x** 14+1400*x**13-480*x**12+650*x**11-80*x**10+160*x**9-5*x**8+20*x**7+x**5+25 6*x**3-768*x**2-64)/((x**20-20*x**19+160*x**18-640*x**17+1280*x**16-1024*x **15)*exp(4)**5+(-5*x**20+100*x**19-800*x**18+3205*x**17-6480*x**16+5600*x **15-1280*x**14+1280*x**13)*exp(4)**4+(10*x**20-200*x**19+1600*x**18-6420* x**17+13120*x**16-12160*x**15+5130*x**14-5240*x**13+480*x**12-640*x**11)*e xp(4)**3+(-10*x**20+200*x**19-1600*x**18+6430*x**17-13280*x**16+13120*x**1 5-7710*x**14+8040*x**13-1440*x**12+1930*x**11-80*x**10+160*x**9)*exp(4)**2 +(5*x**20-100*x**19+800*x**18-3220*x**17+6720*x**16-7040*x**15+5150*x**14- 5480*x**13+1440*x**12-1940*x**11+160*x**10-320*x**9+5*x**8-20*x**7)*exp(4) -x**20+20*x**19-160*x**18+645*x**17-1360*x**16+1504*x**15-1290*x**14+1400* x**13-480*x**12+650*x**11-80*x**10+160*x**9-5*x**8+20*x**7+x**5),x)
x + 16/(x**16*(-4*exp(12) - 4*exp(4) + 1 + 6*exp(8) + exp(16)) + x**15*(-1 6*exp(16) - 96*exp(8) - 16 + 64*exp(4) + 64*exp(12)) + x**14*(-384*exp(12) - 384*exp(4) + 96 + 576*exp(8) + 96*exp(16)) + x**13*(-256*exp(16) - 1548 *exp(8) - 260 + 1036*exp(4) + 1028*exp(12)) + x**12*(-1072*exp(12) - 1168* exp(4) + 304 + 1680*exp(8) + 256*exp(16)) + x**11*(-576*exp(8) - 192 + 576 *exp(4) + 192*exp(12)) + x**10*(-256*exp(12) - 780*exp(4) + 262 + 774*exp( 8)) + x**9*(-48*exp(8) - 48 + 96*exp(4)) + x**8*(-192*exp(4) + 96 + 96*exp (8)) + x**7*(-4 + 4*exp(4)) + x**6*(16 - 16*exp(4)) + x**4)
Leaf count of result is larger than twice the leaf count of optimal. 198 vs. \(2 (23) = 46\).
Time = 0.26 (sec) , antiderivative size = 198, normalized size of antiderivative = 8.25 \[ \int \frac {-64-768 x^2+256 x^3+x^5+20 x^7-5 x^8+160 x^9-80 x^{10}+650 x^{11}-480 x^{12}+1400 x^{13}-1290 x^{14}+1504 x^{15}-1360 x^{16}+645 x^{17}-160 x^{18}+20 x^{19}-x^{20}+e^8 \left (160 x^9-80 x^{10}+1930 x^{11}-1440 x^{12}+8040 x^{13}-7710 x^{14}+13120 x^{15}-13280 x^{16}+6430 x^{17}-1600 x^{18}+200 x^{19}-10 x^{20}\right )+e^{16} \left (1280 x^{13}-1280 x^{14}+5600 x^{15}-6480 x^{16}+3205 x^{17}-800 x^{18}+100 x^{19}-5 x^{20}\right )+e^{20} \left (-1024 x^{15}+1280 x^{16}-640 x^{17}+160 x^{18}-20 x^{19}+x^{20}\right )+e^4 \left (768 x^2-256 x^3-20 x^7+5 x^8-320 x^9+160 x^{10}-1940 x^{11}+1440 x^{12}-5480 x^{13}+5150 x^{14}-7040 x^{15}+6720 x^{16}-3220 x^{17}+800 x^{18}-100 x^{19}+5 x^{20}\right )+e^{12} \left (-640 x^{11}+480 x^{12}-5240 x^{13}+5130 x^{14}-12160 x^{15}+13120 x^{16}-6420 x^{17}+1600 x^{18}-200 x^{19}+10 x^{20}\right )}{x^5+20 x^7-5 x^8+160 x^9-80 x^{10}+650 x^{11}-480 x^{12}+1400 x^{13}-1290 x^{14}+1504 x^{15}-1360 x^{16}+645 x^{17}-160 x^{18}+20 x^{19}-x^{20}+e^8 \left (160 x^9-80 x^{10}+1930 x^{11}-1440 x^{12}+8040 x^{13}-7710 x^{14}+13120 x^{15}-13280 x^{16}+6430 x^{17}-1600 x^{18}+200 x^{19}-10 x^{20}\right )+e^{16} \left (1280 x^{13}-1280 x^{14}+5600 x^{15}-6480 x^{16}+3205 x^{17}-800 x^{18}+100 x^{19}-5 x^{20}\right )+e^{20} \left (-1024 x^{15}+1280 x^{16}-640 x^{17}+160 x^{18}-20 x^{19}+x^{20}\right )+e^4 \left (-20 x^7+5 x^8-320 x^9+160 x^{10}-1940 x^{11}+1440 x^{12}-5480 x^{13}+5150 x^{14}-7040 x^{15}+6720 x^{16}-3220 x^{17}+800 x^{18}-100 x^{19}+5 x^{20}\right )+e^{12} \left (-640 x^{11}+480 x^{12}-5240 x^{13}+5130 x^{14}-12160 x^{15}+13120 x^{16}-6420 x^{17}+1600 x^{18}-200 x^{19}+10 x^{20}\right )} \, dx=x + \frac {16}{x^{16} {\left (e^{16} - 4 \, e^{12} + 6 \, e^{8} - 4 \, e^{4} + 1\right )} - 16 \, x^{15} {\left (e^{16} - 4 \, e^{12} + 6 \, e^{8} - 4 \, e^{4} + 1\right )} + 96 \, x^{14} {\left (e^{16} - 4 \, e^{12} + 6 \, e^{8} - 4 \, e^{4} + 1\right )} - 4 \, x^{13} {\left (64 \, e^{16} - 257 \, e^{12} + 387 \, e^{8} - 259 \, e^{4} + 65\right )} + 16 \, x^{12} {\left (16 \, e^{16} - 67 \, e^{12} + 105 \, e^{8} - 73 \, e^{4} + 19\right )} + 192 \, x^{11} {\left (e^{12} - 3 \, e^{8} + 3 \, e^{4} - 1\right )} - 2 \, x^{10} {\left (128 \, e^{12} - 387 \, e^{8} + 390 \, e^{4} - 131\right )} - 48 \, x^{9} {\left (e^{8} - 2 \, e^{4} + 1\right )} + 96 \, x^{8} {\left (e^{8} - 2 \, e^{4} + 1\right )} + 4 \, x^{7} {\left (e^{4} - 1\right )} - 16 \, x^{6} {\left (e^{4} - 1\right )} + x^{4}} \]
integrate(((x^20-20*x^19+160*x^18-640*x^17+1280*x^16-1024*x^15)*exp(4)^5+( -5*x^20+100*x^19-800*x^18+3205*x^17-6480*x^16+5600*x^15-1280*x^14+1280*x^1 3)*exp(4)^4+(10*x^20-200*x^19+1600*x^18-6420*x^17+13120*x^16-12160*x^15+51 30*x^14-5240*x^13+480*x^12-640*x^11)*exp(4)^3+(-10*x^20+200*x^19-1600*x^18 +6430*x^17-13280*x^16+13120*x^15-7710*x^14+8040*x^13-1440*x^12+1930*x^11-8 0*x^10+160*x^9)*exp(4)^2+(5*x^20-100*x^19+800*x^18-3220*x^17+6720*x^16-704 0*x^15+5150*x^14-5480*x^13+1440*x^12-1940*x^11+160*x^10-320*x^9+5*x^8-20*x ^7-256*x^3+768*x^2)*exp(4)-x^20+20*x^19-160*x^18+645*x^17-1360*x^16+1504*x ^15-1290*x^14+1400*x^13-480*x^12+650*x^11-80*x^10+160*x^9-5*x^8+20*x^7+x^5 +256*x^3-768*x^2-64)/((x^20-20*x^19+160*x^18-640*x^17+1280*x^16-1024*x^15) *exp(4)^5+(-5*x^20+100*x^19-800*x^18+3205*x^17-6480*x^16+5600*x^15-1280*x^ 14+1280*x^13)*exp(4)^4+(10*x^20-200*x^19+1600*x^18-6420*x^17+13120*x^16-12 160*x^15+5130*x^14-5240*x^13+480*x^12-640*x^11)*exp(4)^3+(-10*x^20+200*x^1 9-1600*x^18+6430*x^17-13280*x^16+13120*x^15-7710*x^14+8040*x^13-1440*x^12+ 1930*x^11-80*x^10+160*x^9)*exp(4)^2+(5*x^20-100*x^19+800*x^18-3220*x^17+67 20*x^16-7040*x^15+5150*x^14-5480*x^13+1440*x^12-1940*x^11+160*x^10-320*x^9 +5*x^8-20*x^7)*exp(4)-x^20+20*x^19-160*x^18+645*x^17-1360*x^16+1504*x^15-1 290*x^14+1400*x^13-480*x^12+650*x^11-80*x^10+160*x^9-5*x^8+20*x^7+x^5),x, algorithm=\
x + 16/(x^16*(e^16 - 4*e^12 + 6*e^8 - 4*e^4 + 1) - 16*x^15*(e^16 - 4*e^12 + 6*e^8 - 4*e^4 + 1) + 96*x^14*(e^16 - 4*e^12 + 6*e^8 - 4*e^4 + 1) - 4*x^1 3*(64*e^16 - 257*e^12 + 387*e^8 - 259*e^4 + 65) + 16*x^12*(16*e^16 - 67*e^ 12 + 105*e^8 - 73*e^4 + 19) + 192*x^11*(e^12 - 3*e^8 + 3*e^4 - 1) - 2*x^10 *(128*e^12 - 387*e^8 + 390*e^4 - 131) - 48*x^9*(e^8 - 2*e^4 + 1) + 96*x^8* (e^8 - 2*e^4 + 1) + 4*x^7*(e^4 - 1) - 16*x^6*(e^4 - 1) + x^4)
Leaf count of result is larger than twice the leaf count of optimal. 81 vs. \(2 (23) = 46\).
Time = 0.31 (sec) , antiderivative size = 81, normalized size of antiderivative = 3.38 \[ \int \frac {-64-768 x^2+256 x^3+x^5+20 x^7-5 x^8+160 x^9-80 x^{10}+650 x^{11}-480 x^{12}+1400 x^{13}-1290 x^{14}+1504 x^{15}-1360 x^{16}+645 x^{17}-160 x^{18}+20 x^{19}-x^{20}+e^8 \left (160 x^9-80 x^{10}+1930 x^{11}-1440 x^{12}+8040 x^{13}-7710 x^{14}+13120 x^{15}-13280 x^{16}+6430 x^{17}-1600 x^{18}+200 x^{19}-10 x^{20}\right )+e^{16} \left (1280 x^{13}-1280 x^{14}+5600 x^{15}-6480 x^{16}+3205 x^{17}-800 x^{18}+100 x^{19}-5 x^{20}\right )+e^{20} \left (-1024 x^{15}+1280 x^{16}-640 x^{17}+160 x^{18}-20 x^{19}+x^{20}\right )+e^4 \left (768 x^2-256 x^3-20 x^7+5 x^8-320 x^9+160 x^{10}-1940 x^{11}+1440 x^{12}-5480 x^{13}+5150 x^{14}-7040 x^{15}+6720 x^{16}-3220 x^{17}+800 x^{18}-100 x^{19}+5 x^{20}\right )+e^{12} \left (-640 x^{11}+480 x^{12}-5240 x^{13}+5130 x^{14}-12160 x^{15}+13120 x^{16}-6420 x^{17}+1600 x^{18}-200 x^{19}+10 x^{20}\right )}{x^5+20 x^7-5 x^8+160 x^9-80 x^{10}+650 x^{11}-480 x^{12}+1400 x^{13}-1290 x^{14}+1504 x^{15}-1360 x^{16}+645 x^{17}-160 x^{18}+20 x^{19}-x^{20}+e^8 \left (160 x^9-80 x^{10}+1930 x^{11}-1440 x^{12}+8040 x^{13}-7710 x^{14}+13120 x^{15}-13280 x^{16}+6430 x^{17}-1600 x^{18}+200 x^{19}-10 x^{20}\right )+e^{16} \left (1280 x^{13}-1280 x^{14}+5600 x^{15}-6480 x^{16}+3205 x^{17}-800 x^{18}+100 x^{19}-5 x^{20}\right )+e^{20} \left (-1024 x^{15}+1280 x^{16}-640 x^{17}+160 x^{18}-20 x^{19}+x^{20}\right )+e^4 \left (-20 x^7+5 x^8-320 x^9+160 x^{10}-1940 x^{11}+1440 x^{12}-5480 x^{13}+5150 x^{14}-7040 x^{15}+6720 x^{16}-3220 x^{17}+800 x^{18}-100 x^{19}+5 x^{20}\right )+e^{12} \left (-640 x^{11}+480 x^{12}-5240 x^{13}+5130 x^{14}-12160 x^{15}+13120 x^{16}-6420 x^{17}+1600 x^{18}-200 x^{19}+10 x^{20}\right )} \, dx=\frac {x e^{20} - 5 \, x e^{16} + 10 \, x e^{12} - 10 \, x e^{8} + 5 \, x e^{4} - x}{e^{20} - 5 \, e^{16} + 10 \, e^{12} - 10 \, e^{8} + 5 \, e^{4} - 1} + \frac {16}{{\left (x^{4} e^{4} - x^{4} - 4 \, x^{3} e^{4} + 4 \, x^{3} + x\right )}^{4}} \]
integrate(((x^20-20*x^19+160*x^18-640*x^17+1280*x^16-1024*x^15)*exp(4)^5+( -5*x^20+100*x^19-800*x^18+3205*x^17-6480*x^16+5600*x^15-1280*x^14+1280*x^1 3)*exp(4)^4+(10*x^20-200*x^19+1600*x^18-6420*x^17+13120*x^16-12160*x^15+51 30*x^14-5240*x^13+480*x^12-640*x^11)*exp(4)^3+(-10*x^20+200*x^19-1600*x^18 +6430*x^17-13280*x^16+13120*x^15-7710*x^14+8040*x^13-1440*x^12+1930*x^11-8 0*x^10+160*x^9)*exp(4)^2+(5*x^20-100*x^19+800*x^18-3220*x^17+6720*x^16-704 0*x^15+5150*x^14-5480*x^13+1440*x^12-1940*x^11+160*x^10-320*x^9+5*x^8-20*x ^7-256*x^3+768*x^2)*exp(4)-x^20+20*x^19-160*x^18+645*x^17-1360*x^16+1504*x ^15-1290*x^14+1400*x^13-480*x^12+650*x^11-80*x^10+160*x^9-5*x^8+20*x^7+x^5 +256*x^3-768*x^2-64)/((x^20-20*x^19+160*x^18-640*x^17+1280*x^16-1024*x^15) *exp(4)^5+(-5*x^20+100*x^19-800*x^18+3205*x^17-6480*x^16+5600*x^15-1280*x^ 14+1280*x^13)*exp(4)^4+(10*x^20-200*x^19+1600*x^18-6420*x^17+13120*x^16-12 160*x^15+5130*x^14-5240*x^13+480*x^12-640*x^11)*exp(4)^3+(-10*x^20+200*x^1 9-1600*x^18+6430*x^17-13280*x^16+13120*x^15-7710*x^14+8040*x^13-1440*x^12+ 1930*x^11-80*x^10+160*x^9)*exp(4)^2+(5*x^20-100*x^19+800*x^18-3220*x^17+67 20*x^16-7040*x^15+5150*x^14-5480*x^13+1440*x^12-1940*x^11+160*x^10-320*x^9 +5*x^8-20*x^7)*exp(4)-x^20+20*x^19-160*x^18+645*x^17-1360*x^16+1504*x^15-1 290*x^14+1400*x^13-480*x^12+650*x^11-80*x^10+160*x^9-5*x^8+20*x^7+x^5),x, algorithm=\
(x*e^20 - 5*x*e^16 + 10*x*e^12 - 10*x*e^8 + 5*x*e^4 - x)/(e^20 - 5*e^16 + 10*e^12 - 10*e^8 + 5*e^4 - 1) + 16/(x^4*e^4 - x^4 - 4*x^3*e^4 + 4*x^3 + x) ^4
Timed out. \[ \int \frac {-64-768 x^2+256 x^3+x^5+20 x^7-5 x^8+160 x^9-80 x^{10}+650 x^{11}-480 x^{12}+1400 x^{13}-1290 x^{14}+1504 x^{15}-1360 x^{16}+645 x^{17}-160 x^{18}+20 x^{19}-x^{20}+e^8 \left (160 x^9-80 x^{10}+1930 x^{11}-1440 x^{12}+8040 x^{13}-7710 x^{14}+13120 x^{15}-13280 x^{16}+6430 x^{17}-1600 x^{18}+200 x^{19}-10 x^{20}\right )+e^{16} \left (1280 x^{13}-1280 x^{14}+5600 x^{15}-6480 x^{16}+3205 x^{17}-800 x^{18}+100 x^{19}-5 x^{20}\right )+e^{20} \left (-1024 x^{15}+1280 x^{16}-640 x^{17}+160 x^{18}-20 x^{19}+x^{20}\right )+e^4 \left (768 x^2-256 x^3-20 x^7+5 x^8-320 x^9+160 x^{10}-1940 x^{11}+1440 x^{12}-5480 x^{13}+5150 x^{14}-7040 x^{15}+6720 x^{16}-3220 x^{17}+800 x^{18}-100 x^{19}+5 x^{20}\right )+e^{12} \left (-640 x^{11}+480 x^{12}-5240 x^{13}+5130 x^{14}-12160 x^{15}+13120 x^{16}-6420 x^{17}+1600 x^{18}-200 x^{19}+10 x^{20}\right )}{x^5+20 x^7-5 x^8+160 x^9-80 x^{10}+650 x^{11}-480 x^{12}+1400 x^{13}-1290 x^{14}+1504 x^{15}-1360 x^{16}+645 x^{17}-160 x^{18}+20 x^{19}-x^{20}+e^8 \left (160 x^9-80 x^{10}+1930 x^{11}-1440 x^{12}+8040 x^{13}-7710 x^{14}+13120 x^{15}-13280 x^{16}+6430 x^{17}-1600 x^{18}+200 x^{19}-10 x^{20}\right )+e^{16} \left (1280 x^{13}-1280 x^{14}+5600 x^{15}-6480 x^{16}+3205 x^{17}-800 x^{18}+100 x^{19}-5 x^{20}\right )+e^{20} \left (-1024 x^{15}+1280 x^{16}-640 x^{17}+160 x^{18}-20 x^{19}+x^{20}\right )+e^4 \left (-20 x^7+5 x^8-320 x^9+160 x^{10}-1940 x^{11}+1440 x^{12}-5480 x^{13}+5150 x^{14}-7040 x^{15}+6720 x^{16}-3220 x^{17}+800 x^{18}-100 x^{19}+5 x^{20}\right )+e^{12} \left (-640 x^{11}+480 x^{12}-5240 x^{13}+5130 x^{14}-12160 x^{15}+13120 x^{16}-6420 x^{17}+1600 x^{18}-200 x^{19}+10 x^{20}\right )} \, dx=\text {Hanged} \]
int(-(exp(4)*(768*x^2 - 256*x^3 - 20*x^7 + 5*x^8 - 320*x^9 + 160*x^10 - 19 40*x^11 + 1440*x^12 - 5480*x^13 + 5150*x^14 - 7040*x^15 + 6720*x^16 - 3220 *x^17 + 800*x^18 - 100*x^19 + 5*x^20) - exp(20)*(1024*x^15 - 1280*x^16 + 6 40*x^17 - 160*x^18 + 20*x^19 - x^20) - exp(12)*(640*x^11 - 480*x^12 + 5240 *x^13 - 5130*x^14 + 12160*x^15 - 13120*x^16 + 6420*x^17 - 1600*x^18 + 200* x^19 - 10*x^20) + exp(8)*(160*x^9 - 80*x^10 + 1930*x^11 - 1440*x^12 + 8040 *x^13 - 7710*x^14 + 13120*x^15 - 13280*x^16 + 6430*x^17 - 1600*x^18 + 200* x^19 - 10*x^20) - 768*x^2 + 256*x^3 + x^5 + 20*x^7 - 5*x^8 + 160*x^9 - 80* x^10 + 650*x^11 - 480*x^12 + 1400*x^13 - 1290*x^14 + 1504*x^15 - 1360*x^16 + 645*x^17 - 160*x^18 + 20*x^19 - x^20 + exp(16)*(1280*x^13 - 1280*x^14 + 5600*x^15 - 6480*x^16 + 3205*x^17 - 800*x^18 + 100*x^19 - 5*x^20) - 64)/( exp(4)*(20*x^7 - 5*x^8 + 320*x^9 - 160*x^10 + 1940*x^11 - 1440*x^12 + 5480 *x^13 - 5150*x^14 + 7040*x^15 - 6720*x^16 + 3220*x^17 - 800*x^18 + 100*x^1 9 - 5*x^20) + exp(12)*(640*x^11 - 480*x^12 + 5240*x^13 - 5130*x^14 + 12160 *x^15 - 13120*x^16 + 6420*x^17 - 1600*x^18 + 200*x^19 - 10*x^20) + exp(20) *(1024*x^15 - 1280*x^16 + 640*x^17 - 160*x^18 + 20*x^19 - x^20) - exp(8)*( 160*x^9 - 80*x^10 + 1930*x^11 - 1440*x^12 + 8040*x^13 - 7710*x^14 + 13120* x^15 - 13280*x^16 + 6430*x^17 - 1600*x^18 + 200*x^19 - 10*x^20) - x^5 - 20 *x^7 + 5*x^8 - 160*x^9 + 80*x^10 - 650*x^11 + 480*x^12 - 1400*x^13 + 1290* x^14 - 1504*x^15 + 1360*x^16 - 645*x^17 + 160*x^18 - 20*x^19 + x^20 - exp( 16)*(1280*x^13 - 1280*x^14 + 5600*x^15 - 6480*x^16 + 3205*x^17 - 800*x^18 + 100*x^19 - 5*x^20)),x)